Towards Estimating Entrainment Fraction
For Dust Layers
Final Report
Prepared by:
Erdem A. Ural
Loss Prevention Science and Technologies, Inc.
The Fire Protection Research Foundation
One Batterymarch Park
Quincy, MA, USA 02169-7471
Email: [email protected]
http://www.nfpa.org/foundation
© Copyright Fire Protection Research Foundation
June 2011
FOREWORD
Recently there has been an increased awareness of the explosion hazard associated with
combustible dusts. NFPA 654/A.2.2.3.1 includes criteria that have been used for determining
whether an explosion hazard exists in a building compartment. There is, however, genuine
concern over the technical pedigree of those criteria. Recently, federal governmental agencies
have begun using NFPA 654 as a standard for assessing compliance with the General Duty
Clause of the OSH Act of 1970. This has precipitated a genuine concern that the criteria
currently in NFPA 654 do not have sufficient technical justification to be used as a law
enforcement criterion.
The objective of this project is to establish the technical basis for quantitative criteria for
determining that a compartment is a “dust explosion hazard” that can be incorporated into
NFPA 654 and other relevant safety codes and standards. This report presents the results of the
Phase I portion of the study which is the development of a strawman method to assess the dust
hazard.
The content, opinions and conclusions contained in this report are solely those of the author.
Toward Estimating Entrapment Fraction
for Dust Layers
PROJECT TECHNICAL PANEL
Elizabeth Buc, Fire and Materials Research Lab, LLC
Henry Febo, FM Global
Walter Frank, Frank Risk Solutions, Inc.
Paul Hart, XL Global Asset Protection Services
Joseph Senecal, Kidde-Fenwal, Inc.
Martha Curtis, Guy Colonna, NFPA staff liaison
SPONSOR REPRESENTATIVES
Brice Chastain, George Pacific Corporation
Gregory Creswell, Timet
Mark Holcomb, Kimberly-Clark Corporation
Robert Hubbard, Abbott Laboratories
Jerry Jennett, Georgia Gulf Sulfur Corporation
George Olson, Procter & Gamble Company
Samuel Rodgers, Honeywell, Inc.
David Oberholtzer, Henry Sattlethight, The Aluminum Association
PROJECT CONTRACTOR REPRESENTATIVE
Erdem Ural, Loss Prevention Science and Technologies, Inc.
Towards Estimating Entrainment Fraction for Dust Layers
June 10, 2011
Prepared by:
Erdem A. Ural
For:
The Fire Protection Research Foundation
Loss Prevention Science
and Technologies, Inc.
810 Washington Street
Stoughton, MA 02072 USA
Telephone: 781-818-4114
Email: [email protected]
http://www.lpsti.com
LOSS PREVENTION SCIENCE AND TECHNOLOGIES, INC. (LPSTI)
Towards Estimating Entrainment Fraction for Dust Layers
Project Technical Panel
Dust Hazard Threshold Project
Panel Members
Elizabeth Buc, Fire and Materials Research Laboratory
Henry Febo, FM Global
Walt Frank, Frank Risk Consulting
Paul Hart, XL Insurance
Joe Senecal, Kidde Fenwal
Guy Colonna, NFPA staff liaison
Project Sponsor Representatives
Brice Chastain, Georgia Pacific
Greg Creswell, TIMET
Mark Holcomb, Kimberly Clark
Robert Hubbard, Abbott Laboratories
Jerry Jennett, Georgia Gulf Sulfur
David Oberholtzer, Aluminum Association
George Olson, Procter and Gamble
Sam Rodgers, Honeywell
LOSS PREVENTION SCIENCE AND TECHNOLOGIES, INC. (LPSTI)
CAVEAT
The equations analyses and the conclusions
presented in this report are based on a review of
the documents available at the time this report
was prepared. The findings and conclusions in this
report are those of the author and do not
necessarily represent the views of the Fire
Protection Research Foundation or the National
Institute for Occupational Safety and Health.
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Table of Contents
List of Figures
Executive Summary
I. Introduction
II. Literature Review
2.1 An overview of aerodynamic entrainment of dust particles into air
2.2 Characterization of the Aerodynamic Forces Acting on a Solid Particle
2.3 Characterization of the forces Conserving the layer
2.4 Fundamental Studies of Particle Removal from Surfaces
2.5 Applied Research on Aerodynamic Entrainment Threshold
2.6 Applied Research on Aerodynamic Entrainment Mass Flux
2.7 Secondary Explosion Propagation Tests
2.8 Computational Simulation of Aerodynamic Dust Entrainment Phenomena
2.9 Gaps in Available Information
III. Proposed Strawman Method
3.1. An introduction to the Proposed Strawman Methodology
3.2. Estimation of Threshold Entrainment Velocity for Dust
3.3 Estimation of the entrained mass flux
3.4 Comparisons with Large Scale Explosion Data
3.5 Estimation of the dust entrainment caused by primary event scenarios
3.6 Extension of the Strawman Method to Elevated Surfaces
IV. Validation Plan
4.1 Uncertainties in the mass flux correlation
4.2 Recommended test arrangement
4.3 Recommended Test Matrix
V. Acknowledgements
VI. Bibliography
Appendix A. Ad Hoc Methods to Characterize Material Dustiness and Entrainability
A.1 Particle Characterization
A.2 Cohesion Tests
A.3 Terminal Velocity Tests
A.4 Dispersibility Tests
Appendix B. Alternative Mechanism on Dust Cloud Generation
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List of Figures
Figure 1. Different types of sand particle motion that can occur during wind erosion.
Figure 2. Typical streamwise velocity profiles inside the boundary layer: mean
velocity (left), root mean square of the fluctuating velocity (right).
Figure 3. Typical streamwise mean velocity profiles inside the boundary layer for
two different friction coefficients and free stream velocities.
Figure 4. Settling velocity of cornstarch with or without flowability agent Al2O3-C
Figure 5. Prediction of a force-balance theory for spherical sand particles in air.
Figure 6. Threshold shear velocity and suspension modes for wind erosion of sand
Figure 7. Lift-off apparatus to determine the aerodynamic forces required to
remove a dust deposit
Figure 8. Dust removal pattern in the lift-off apparatus.
Figure 9. Comparison of Kalman et al (2005) correlation with data
Figure 10. Shapes of non-spherical particles
Figure 11. Comparison of Kalman et al (2005) correlation with data for glass spheres
and other correlations
Figure 12. Comparison of the predictions from various entrainment mass flux
equations for 53 micron coal dust.
Figure 13. Calculated threshold entrainment velocity as a function of particle size
and particle density
Figure 14. Variation of the minimum threshold velocity and the corresponding optimal
particle size with particle density for nearly spherical particles.
Figure 15. Experimental setup in NIOSH tests. Top: Side view schematics of the mine
geometry, Left: Placing Coal/Rock dust mixtures on the shelves, Right:
distributing dust on the floor.
Figure 16. Measuring the amount of dust scoured during an explosion
Figure 17. Gas velocity recorded near the dust bed during the experimental mine test.
Figure 18. Experimental mine and theoretical dust removal depths for test.
Figure 19. Pressure data from test NGFA56.
Figure 20. Comparison of the cornstarch entrainment predictions with NGFA data.
Figure 21. Hemispherical vessel burst in the middle of the plant.
Figure 22. Peak pressure and velocity fields created by a 74 ft3 hemispherical
enclosure burst at 0.5 bar pressure.
Figure 23. Local peak entrainment mass flux for the 100-micron Aluminum dust
Figure 24. Local entrained mass per unit area for the 100-micron Aluminum dust
Figure 25. Conceptual schematics of vent discharge treated as half a round floor jet
Figure 26. Peak velocity field, and the discharge width created by the example
worked out for Scenario B.
Figure 27. Local peak entrainment mass flux for the Example worked out for Scenario B.
Figure 28. Local entrained mass per unit area for the Example worked out for Scenario B.
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Executive Summary
This report describes the work performed in the first phase of the Fire Protection Research
Foundation project entitled Dust Explosion Hazard Assessment Methodology.
Dust explosions occur only when a number of preceding events take place almost
simultaneously. A comprehensive generic chain of events that can lead to an explosion is
described in Chapter 17-8 of NFPA Handbook of Fire Protection.
Unless dust is kept suspended in the air by design, most dust explosions start with a disturbance
that raises dust into suspension. The disturbance could be as simple as the rupture of a
compressed air line, a mechanical jolt to beams where dust layers have accumulated, or a small
explosion somewhere else in the plant. Once subjected to the disturbance, the amount of dust
entrained (removed) from the deposit depends predominantly on the magnitude and the severity
of the disturbance. Other parameters such dust and layer properties can also play a role on the
dust entrainment rates.
Once the dust is lifted off from the layer, it mixes with air and can form explosible pockets in the
enclosure. The size of the explosible cloud volume is controlled by the dust entrainment rate and
the existing air motion in the enclosure (e.g. ventilation/recirculation), or that induced by the
primary disturbance.
Once created, an explosible dust cloud can be ignited by a number of possible ignition sources.
In critical applications or for hard to ignite dusts, credible strength of ignition sources can be
evaluated and compared to the ignition requirement of the particular dust cloud. Though seldom
done, such an exercise may reveal whether elimination of ignition sources is a viable prevention
method for the particular application. While NFPA standards encourage ignition control to
reduce the frequency of the incidents, they generally assume that an ignition source may exist
despite the presence of an ignition source control program.
Once ignition takes place, the reaction front (flame) moves into the unburnt dust cloud with a
well-defined velocity, called the burning velocity. If the enclosure is practically unvented, the
maximum explosion pressure is related to the heat of combustion of the dust cloud. Fully
confined deflagrations of dust clouds occupying a substantial portion of the enclosure volume
commonly develop pressures in the range of seven to ten times the initial absolute pressure, or
100 to 140 psig (7 to 10 barg). If the enclosure has large openings (deflagration vents), then the
maximum explosion pressure is substantially reduced depending on the burning velocity and the
maximum flame surface area. Pre-existing turbulence conditions inside the enclosure, turbulence
induced by flame propagation, and the geometry of the enclosure can increase both the burning
velocity and the maximum flame surface area.
Process enclosures are seldom designed for pressure containment. Pressures at which enclosure
failure occurs can be quite low, particularly for enclosures of rectangular sheet metal
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construction. These can fail completely at internal pressures of a few pounds per square inch.
Typically, buildings can tolerate only a fraction of 1 psi pressure.
While properly designed deflagration vents can successfully limit the peak pressure rise to a
level that can be tolerated by the enclosure, an explosible dust cloud occupying a substantial
portion of the compartment volume is never allowed in occupied enclosures, because it is
capable of producing untenable conditions in the entire volume. Combustible dust occupancy
standards promulgated by NFPA recognize this fact and impose restrictions on dust
accumulations, currently specified as the threshold layer thickness and areas. For example, the
current (2006) edition of NFPA 654 implies a threshold layer depth of 1/32 inch while NFPA
664 uses a layer depth of 1/8 inch. NFPA 654 permits adjusting the layer depth criterion for
variations in dust bulk density while NFPA 664 does not.
The objective of this project is to establish the technical basis for quantitative criteria for
determining that a compartment is a dust explosion hazard that can be incorporated into NFPA
standards or other relevant safety codes. For the purpose of this study, a dust explosion
hazardous condition is defined as that which creates a hazard for individuals and property, which
are not intimate with the initiating event. The scope of the first phase of the project is limited to a
study of those combustible dusts covered under the scopes of NFPA Standards 61, 484, 654 and
664 which include dusts encountered in agricultural and food processing, combustible metals,
wood processing and wood-working facilities. However, since these standards cover dusts
exhibiting a wide spectrum of properties, the project results could be extrapolated to most other
dusts. In fact, large scale test data for coal dust rock dust mixtures as well as sand and soil were
used in the preliminary validation of the strawman method described in this report.
As apparent from the objective, the biggest challenge in a project of this sort is to simplify the
models to an extent that would be suitable for incorporation in NFPA Standards and Codes. This
is a difficult task to accomplish for two reasons:
1) the level of complication that is suitable for incorporation in NFPA Standards is at best a
subjective concept, and
2) simplification often comes at a cost of loss of generality, and added conservatism for
some applications.
Many valuable discussions with the project panel helped the author develop a strawman method
which provides a good balance between the two desirable but competing features: simplicity
versus generality.
Acceptable simplicity was achieved by assuming all entrained dust enters into a dust cloud,
which is always at the worst-case concentration for the particular combustible dust. The more
dust is entrained, the bigger the cloud is. This assumption is conservative but obviates the need
for complex tools such as computational fluid dynamics to calculate the development of the
entrained dust cloud. This assumption also allows ready use of the partial volume deflagration
concepts and equations provided in NFPA 68, a published consensus standard.
Hence, the strawman method is essentially reduced to two components:
a. selection of the types, magnitudes and durations of the maximum credible disturbances
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b. calculation of the mass of the dust entrained from the deposits.
The first component depends on the primary event scenarios that are credible for the specific
occupancy and are expected to evolve through the consensus process. To demonstrate the
concepts in this report, two most common scenarios were selected after conferring with the
project panel.
First scenario is the catastrophic burst of indoor equipment. Resulting blast wave propagates over
the dust layer and raises all of it or a portion of it into suspension. A worked out example
included in the report demonstrates how the amount of dust lifted from the layer can be estimated
by relying on published pressure vessel burst nomograms to calculate the magnitude of the air
velocity pulse and its duration.
The second scenario is the deflagration venting from a room into a building covered with
combustible dust deposits. In the worked out example included in the report, the flow field
induced by the vent discharge is approximated by using axial jet correlations, and its duration is
calculated using an equation provided in NFPA 68.
The second component of the strawman method is the calculation of the mass of the dust
entrained from the deposits. An extensive international literature review was carried out on
relevant research on airflow induced dust entrainment rates. Effects of factors such as
aerodynamic flow and boundary layer characteristics, dust particle size and shape, and
dispersibility were examined. Since the dust entrainment occurs deep in the boundary layer,
friction velocity rather than the free stream velocity is the more appropriate parameter to
correlate the entrainment rate. On the other hand, most users of the NFPA standards are not
anticipated to be versatile in using aerodynamics concepts encompassing the friction velocity.
Therefore, an additional simplification is introduced by translating the selected entrainment rate
correlation to free stream velocity. The selected equation was also modified for low flow
velocities so that entrainment rate tends to zero at the threshold velocity.
The following equation is proposed to estimate the entrainment mass flux1 until the validation
tests are completed in the next phase of this project:
m” = 0.002*ρ*U*(U1/2 - Ut2 / U3/2)
U > Ut
(1)
where:
m” entrained mass flux in kg/m2-s
ρ gas density in kg/m3
U free stream velocity in m/s
Ut threshold velocity in m/s.
The threshold velocity, Ut, is the minimum air velocity at which dust removal from the layer
begins, and it depends on factors such as particle size, particle shape and particle density. The
report provides algebraic correlations and charts to estimate this parameter.
1
The rate of mass removal per unit area per unit time.
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Predictions of the strawman method is compared to available large scale coal dust and cornstarch
explosion test data. Good agreement was observed. Nevertheless, additional tests are
recommended to validate equation (1) further.
The new strawman method described in this report represents a paradigm shift in dust explosion
hazard assessment. The approach used in current NFPA standards implicitly assumes that the
dust explosion hazard is primarily related to the thickness of the dust layers, or the total mass of
the dust accumulations. The new strawman method, on the other hand, primarily determines the
maximum amount of dust an initial disturbance can raise into a cloud. If that quantity is large
enough to create an explosion risk, then the explosion hazard can still be averted by controlling
the amount of dust accumulations.
In other words, the new strawman method is capable of estimating the fraction of the dust
accumulations that can become airborne, a parameter also known as the entrainment fraction.
Predicted entrainment fraction values range anywhere from zero to one, depending on a number
of parameters including dust characteristics, layer thickness, geometry, as well as type,
magnitude and the duration of the maximum credible disturbance.
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I
Introduction
The objective of this project was originally specified as to “perform literature review on relevant
research and dust explosion incidents focused on those factors which impact the dust hazard
assessment, such as dispersibility (entrainability), layer thickness and entrainment characteristics
of dust particles, facility geometry and deposition characteristics, etc.”
During the teleconference held on October 6, 2009, project panel has reviewed the task objective
and refocused it on research and testing, not fire/explosion incidents. NFPA 654 ROC (A2010
published methodologies to determine maximum allowable dust accumulations or minimum
cleaning frequencies. Published formulas rely on an a priori value for the dust entrainment
fraction selected to provide a level of protection, for typical occupancies, comparable to that
implied by the previous editions of NFPA 654. This Research Foundation project focuses on
collecting available information which may be useful to NFPA committees in making informed
decisions about the appropriate value of dust entrainment fraction.
Other tasks of the authorized phase of the project focuses on the development of a proposed
strawman dust explosion hazard assessment method based on those parameters which, if
validated, would be suitable for incorporation in NFPA Standards and Codes.
One of the necessary conditions for the occurrence of dust explosions is the dispersion of
combustible dust in air. In industrial situations, dust dispersion could be (Hertzberg, 1987):
(1)
an integral part of the process, as in a pulverizer, or a pneumatic transport line;
(2)
a by-product of the process, as in dust handling equipment; or
(3)
caused by an accident such as a ruptured compressed air line, or a blast wave
emanated from a nearby explosion.
In the first category, efficient dispersion of dust is wanted, in the second category, the dust
dispersion is considered a nuisance, mostly from the industrial hygiene point of view, and
suppression techniques such as wetting or oil mist treatments2 are employed. The types of
accidents included in the third category may suspend large quantities of combustible dust in air
for relatively short periods, and may lead to severe dust explosions. For suitable plant geometry
and fuel distribution, even a mild primary dust explosion may lead to cascading “secondary
explosions” in which the aerodynamic disturbance caused by the primary explosion lifts the dust
originally deposited on surfaces and mixes it with the air, thereby creating additional paths of
flammable dust-air mixture for the flame to travel. Multiple secondary explosions are not
uncommon in industrial dust explosions and can be responsible for severe losses. For example,
based on detailed investigations of fourteen grain elevator explosions occurring between January
1979 and April 1981, Kauffman (1987) attributes, on the average, 85% of the fatalities, 89% of
2
These additives cause an increase in the cohesion of the particles in the layer, thereby requiring stronger
disturbance for their entrainment. Treated dust also tend to peel as large agglomerates rather than individual
particles, which tend to settle out faster. Dust abatement techniques of this type have been in use in a number
industries such as grain, coal and chemical.
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the injuries, and 96% of the property loss to secondary explosions, with primary explosions
making up the small balance. Similar conclusions are drawn from the recent CSB investigations.
Accumulations of dust inside enclosures are normally found on the floor, as well as on other
surfaces such as beams, equipment and structural elements. The elevation of the surfaces covered
by dust layers can be expected to affect the dust cloud size and concentration, since the
gravitational force tends to reduce the dispersion, if the dust accumulations are close to the floor,
and aid it, if they are close to the ceiling. In the first case, the energy to overcome gravity must
be supplied by the disturbance.
The disturbance created by the primary explosion could be of aerodynamic nature or in the form
of vibrations transmitted by solid structures. While vibrations can be responsible for dispersal of
some of the dust located near the top of an enclosure or components possessing just the right
degree of stiffness and mass, most dust is usually dispersed by the aerodynamic disturbance. This
disturbance is of the transient type and can last anywhere from a fraction of a second to several
seconds. For a secondary explosion to be possible, the disturbance must be of sufficient strength
and duration to:
1.
2.
3.
remove dust particles from the layer;
mix the dust with air to form a flammable (explosible) dust cloud; and
prevent the dust cloud from settling until it is ignited by local ignition sources or
by the arrival of a flame front propagating from the primary explosion.
Hence, the primary focus of this project is on the removal by aerodynamic disturbances of dust
particles or agglomerates from layers or piles of cohesive and non-cohesive dusts of varying
particle shapes and densities.
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II
Literature Review
2.1 An overview of aerodynamic entrainment of dust particles into air
Aerodynamic forces acting on a dust layer can dislodge particles or clumps of particles from the
layer and set them into motion. The entrainment of dust layers occurs in various modes or their
combinations. Powders demonstrating negligible cohesion3 tend to be removed as individual
particles. More cohesive powders are removed as groups of particles (agglomerates), and
sometimes, depending on layer and surface properties, appreciable portions of the layer can be
lifted as a whole.
When the entire layer is subjected to uniform aerodynamic conditions (as in the case of pipe
flow, or atmospheric flow) the dust may either be removed uniformly over the entire layer
(erosion), or may be removed from the leading edge of the deposit. In this latter process called
denudation, the leading edge of the deposit propagates in the direction of the flow. It is generally
believed that for erosion type dust removal, adhesive forces must be larger than the cohesive
forces.
As seen in figure 1, the particles removed from the layer can also show different types of
behavior. Dislodged particles may roll on the surface until they find a spot with reduced fluid
forces (such as a pit) and come to rest, or collide with another particle, thus transferring their
momentum and aiding the removal of the new particle. During their travel, particles may even
become airborne for short periods of time, yet still remain close to the surface. This type of
transport is called surface creep. In another mode of transport called saltation, the particles are
ejected from the surface almost vertically and are carried by the wind horizontally until they fall
back onto the surface. Bagnold (1941) observed saltation layer thicknesses in the order of meters
for desert sand. At higher air velocities, particles do not return to the surface (referred to as
entering into suspension) and are carried for long distances.
Intuitively, it is easy to see whether a particle will be removed from a surface or from another
particle, and the number of particles that get removed per unit time per unit surface area are
governed by a balance between the forces trying to dislodge the particle, and the forces trying to
keep the particle in place.
3
Conventionally, the word cohesion refers to the attraction force between two surfaces of the same material (such as
the dust particles), whereas adhesion implies different materials (such as dust particle attracted to a plate)
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Figure 1. Different types of sand particle motion that can occur during wind erosion (from
Shao, 2008).
2.2 Characterization of the Aerodynamic Forces Acting on a Solid Particle
Extensive reviews of this subject are given by Clift (1978), and Yoshida et al (1979).
Conventionally, aerodynamic force is resolved into two components: drag, in the direction of the
mean flow; and lift, perpendicular to it. For uniform flow over a particle, the drag force is
expressed by
FD = CD A 1/2 ρ U2
(1)
where CD, A, ρ, and U, respectively represent the particle drag coefficient, particle cross—
sectional area, air density, and air velocity with respect to the particle.
At low relative velocities, the drag coefficient decreases with increasing Reynolds
number. For spherical particles, an approximation to drag coefficient for Reynolds numbers
smaller than 1000 is given by (Clift, 1978):
CD = 24/Re (1 + 0.15 Re2/3)
(2)
where:
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Re
D
μ
ρUD/μ particle Reynolds number;
particle diameter;
viscosity of air.
The first term in this equation is called the Stokes drag coefficient, which constitutes the major
portion of the drag for small particles. The corresponding Stokes drag can then be calculated as:
FDst =3 π μ U D
(3)
A classical application of uniform flow over a sphere is the free fall of spheres. The terminal fall
velocity is calculated by equating the drag force to the particle weight. In the Stokes regime (Re
<< 1) this is given by:
Ut = ρp g D2 /(18μ)
(4)
where ρp is the true density of the particle.
At high particle Reynolds numbers, the drag coefficient becomes independent of the Reynolds
number so that the drag force is proportional to the square of both the relative velocity and the
particle size, whereas the terminal velocity is proportional to the square root of the particle size
and density.
The terminal velocity of an ensemble of monodisperse spherical particles in the absence of
agglomeration is lower than that measured for an individual particle. This hindered settling
problem has been studied in detail for monodisperse and polydisperse suspensions. Examples of
such work can be found in Batchelor (1972), Batchelor and Wen (1982), and Davis and Birdsell
(1988). The correction in the terminal velocity due to hindered settling is of the same order of
magnitude as the volumetric fraction of the solid particles and should be negligible for most
explosible dust clouds.
The drag force for low Reynolds number shear flow around a spherical particle is usually
calculated by assuming the relative flow velocity as the undisturbed value at the particle center.
This is rigorously accurate only for small particles exposed to constant velocity gradient because
the Stokes drag force is proportional to the relative velocity. If the particle is adjacent to a wall,
however, the drag force can be 70% higher than the Stokes drag, as suggested by the creeping
flow solution of O’Neill (1968):
FDw = 8 μ γ D2
(5)
where γ denotes the velocity gradient perpendicular to the wall. The effect of flow shear on
particle drag is more difficult to assess at high Reynolds numbers due to flow separation
phenomenon.
The lift force on a spherical particle is induced if the particle is rotating (axis of rotation
perpendicular to the direction of flow) or is subjected to shear flow. Most work on this topic is
concentrated on either very low or very high Reynolds numbers.
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The lift force on a sphere spinning in a uniform flow was calculated for small Reynolds numbers
by Rubinow and Keller (1961) as:
L = 1/8 π ρ D3 U ω
(6)
where ω is the angular spin velocity. It is interesting to note that this solution is independent of
viscosity, and is in a form similar to the Kutta—Joukowsky formula used to predict lift due to
potential flow.
Saffman (1965) calculated a lift force exerted on a spherical particle by a shear flow. The
formula he developed for low Reynolds numbers:
L = 1.61 ρ ν1/2 γ1/2 D2 U
(7)
where γ is the magnitude of the velocity gradient. Saffman’s analysis has shown that up to the
maximum spin attainable by free particles due to shear, the effect of angular velocity on the lift
force is of higher order than the that calculated from the above equation. The velocity, U, in this
equation is taken as the undisturbed velocity at the particle center. For a particle resting on a flat
surface U = γ D/2, therefore:
Lw = 0.8 ρ ν1/2 γ3/2 D3
(8)
Another small Reynolds number particle lift mechanism was postulated by Cleaver and Yates
(1973) for turbulent boundary layers. This model is based on the turbulent burst phenomenon
occurring as sudden random eruptions in the boundary layer, transporting fluid near the wall
towards the mean flow. Treating bursts as viscous stagnation flow, and somehow estimating the
strength of the stagnation flow from the measurements of the mean velocity fluctuations normal
to the wall, Cleaver and Yates (1973) proposed the following formula for particle lift due to
turbulent burst:
L = 0.076 ρ ν1/2 γ3/2 D3
(9)
which is an order of magnitude smaller than the Saffman’s lift.
The lift due to particle spin in uniform flow at high Reynolds numbers, called the Magnus force
after its inventor, is well known to many tennis and golf players. The magnitude of this force is
determined experimentally (see e.g., Clift (1978)), since the lift is generated by the formation of
an asymmetric wake.
A sphere resting on a flat plate also experiences a lift force, as well as increased drag due to the
presence of the wall, at high Reynolds numbers. Okamoto (1979) measured a lift coefficient CL =
0.242, and drag coefficient CD = 0.627 at Re = 4.74 x 104.
The free stream turbulence is expected to have an important effect in the dispersion of a dust
cloud once the particles are removed from the surface because it may control the extent of
dispersion, settling rate and agglomeration/deagglomeration phenomena. A review of free stream
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turbulence effects on single particle behavior is given by Clift (1978). The particle dispersion by
turbulence field is believed to be strongly dependent on the Stokes number, which is defined as
the ratio of the characteristic particle response time to the time scale of the large scale eddies.
The characteristic particle response time can be estimated as the ratio of terminal velocity to
gravitational acceleration. At low Stokes numbers (i.e., particles with small settling velocity), the
particles faithfully follow the fluid motion, and they are dispersed at approximately the fluid
diffusion rate. At large Stokes numbers there is hardly any particle dispersion. Interestingly,
there is an intermediate Stokes number regime in which particles may be dispersed faster than
the fluid would, believed to be due to particles actually flinging out of eddies (e.g., Chein and
Chung (1988)).
At intermediate—to—high Stokes numbers, mean particle drag may be decreased or increased
due to presence of turbulence. Transition of flow around particle to turbulence is known to
sharply reduce the drag coefficient. The presence of free stream turbulence causes this transition
to occur at lower Reynolds numbers than critical. One of the mechanisms of increased particle
drag is observed beyond the Stokes regime where the particle drag is a stronger than linear
function of relative velocity. As a result of this functional dependence, a particle subjected to
sinusoidal velocity fluctuations superposed on a mean flow should experience a larger increase
in drag force during positive phase compared to the decrease in drag during the negative phase.
When averaged over the cycle, therefore, a net increase in drag arises. As a result, a decrease in
terminal velocity is observed in a fluctuating flow field. If the velocity fluctuations are of
sufficient strength, the average terminal velocity reaches zero. The former phenomenon, called
levitation, has been observed for solid particles suspended in liquid (Krantz et al (1973)).
In practically all scenarios of interest to this project, dust layers are formed over impermeable
surfaces, and the disturbing air is forced to flow parallel to the solid boundary. The no-slip flow
condition at the boundary inevitably imposes a boundary layer type flow phenomenon around the
dust layer. Figure 2 shows a boundary layer velocity profile typical for turbulent flow in the
absence of dust entraiment. Figure 2 also shows the profile of root mean square streamwise
velocity fluctuation which tends to be roughly 10% of the free stream velocity (Schlichting,
1968). As a rule of thumb, the peak of the root mean square transversal velocity fluctuation is
roughly 5% of the free stream velocity, and occurs at a greater distance from the wall. The latter
fluctuation component is a mechanism aiding migration of entrained particles away from the
layer.
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Figure 2. Typical streamwise velocity profiles inside the boundary layer: mean velocity
(left), root mean square of the fluctuating velocity (right).
y
U1
U2
u
Figure 3. Typical streamwise mean velocity profiles inside the boundary layer for two
different friction coefficients and free stream velocities.
The foregoing discussion suggests that aerodynamic forces acting on particles in a dust layer
increase with increasing free-stream velocity. In early studies, the entrainment threshold or the
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entrainment amount had been correlated to the free stream velocity. In reality, small dust
particles of interest here fall deep into the boundary layer as shown in Figure 3. As a result, the
layer is affected by the velocity gradient (or the boundary layer thickness) more so than the free
stream velocity. That is why, in modern studies, the entrainment threshold or the entrainment
amount had been correlated to the velocity gradient (γ), the shear stress (τw), or the friction
velocity (interchangeably termed u*, Uf or uτ). By definition, these three parameters are uniquely
related to each other through:
τw = μ γ = ρ uτ2
(10)
It is also conventional to define a friction coefficient, Cfo relating the friction velocity (uτ) to the
free stream velocity (Ue) through:
τw = Cfo 1/2 ρ Ue2
(11)
Where the subscript o designates the friction coefficient in the absence of dust entrainment.
The presence of a dust cloud in suspension complicates the turbulence field. The dispersed phase
affects both the mean and fluctuating components of the flow field. A review of this subject can
be found in Faeth (1987). As will be discussed later, the entrainment process also effects the
boundary layer properties.
The scope of this discussion thus far is limited to spherical particles. Most real particles,
however, are of non-spherical shape, which introduces another source of uncertainty to the
analyses. Depending on the profiles they present, non-spherical particles can generate significant
lift forces. Correction factors to the drag coefficient of some special cases of non-spherical
particles have been developed; a review of this topic was given in Carmichael (1984).
Ural (1989) developed a test method to measure the settling velocity distribution of dust samples.
Typical data is shown in Figure 4 for corn starch with or without electrical conductivity additive.
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Figure 4. Settling velocity of cornstarch with or without flowability agent Al2O3-C
2.3 Characterization of the forces Conserving the layer
For horizontal layers, gravity holds the particles in place. The weight of a spherical particle can
be calculated from:
W = 1/6 π ρp D3
(12)
Other forces include adhesion/cohesion, chemical bonds and mechanical interlocking (as in long
fibers). Frequently cited classical reviews of this topic include Corn (1966), and Zimon (1982).
Various methods have been used to measure the adhesive forces. When the adhesive force is
smaller than the particle weight, the adhesive force can be determined from the tilting angle of
the surface at the time particles fall. Similarly, in the pendulum method a particle is attached to a
fiber and hangs freely. A surface (or another particle to measure cohesion) is placed in contact
with the suspended particle, and then pulled away in a direction perpendicular to the suspending
fiber, until the particle detaches from the surface. The adhesion force is calculated from the slope
of the fiber at the moment of detachment. For larger adhesive forces, microbalance techniques
are used where the particle is attached to a micro-force measurement system (which can be an
electronic balance, a spring, or a cantilevered beam). Both the pendulum and microbalance
techniques are limited to relatively large particle sizes because small particles are very difficult
to attach to the suspending fibers.
Adhesion forces of smaller particles are measured more conveniently using the centrifuge and
the vibration methods. Both methods are capable of measuring adhesive forces up to 106 times
the particle weight.
The studies of adhesion have revealed that for particles of approximately identical size, under
identical conditions, the forces of adhesion will not all be the same; in fact, they may span
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several orders of magnitude. Recognizing this highly statistical nature of the adhesion forces, an
adhesion number is defined as the fraction of particles removed when subjected to a given force.
The statistical nature of the adhesion/cohesion forces is also responsible for the kinetic behavior
of the entrainment flux. In other words, under steady-state exposure to a turbulent aerodynamic
disturbance, entrainment flux changes with time.
From the theoretical standpoint, a number of mechanisms are recognized as playing a role in
adhesion/cohesion of powders in air. Molecules making up the particles possess attractive force
fields (Van der Waals) around them, which in effect, hold them together. The force fields of the
molecules near the particle boundary are not neutralized, thus providing an adhesion force. The
force fields of the individual molecules have been integrated over the particle volume to obtain
the net attraction force between two spherical particles of diameter D1 and D2. The result, called
the Van der Waals Force, is
F
m
α
DD
Z D +D
1
2
⋅
1
1
0
(13)
2
2
where, Z0, the separation distance between the particles, is a major source of uncertainty4 in
determining the molecular forces. The attraction force between a spherical particle (of Diameter
D) and a flat plate can be obtained by allowing D2 to go to infinity:
F
m
α
1
Z
2
⋅D
(14)
0
The constant of proportionality in these equations varies by orders of magnitude for different
materials, and is generally higher for softer material (e.g., plastics versus abrasives) that can
deform and provide an increased contact area. Presence of flaws and trace impurities are also
known to affect the Van der Waals forces. The variation of. the Van der Waals forces under
identical conditions is blamed (Zimon, 1982) on the “energetic inhomogeneity” of solid surfaces,
as well as the microsurface roughness.
The second well studied mechanism of adhesion is due to capillary condensation (also known as
formation of liquid bridges). The water vapor (or solvent vapors) may condense in the vicinity of
contact of two bodies, even when the vapor phase is below saturation, because a negative
curvature exists in the contact area, and the equilibrium vapor pressure is a function of surface
tension and curvature. The condensed liquid forms a film that draws the two bodies together
because of surface tension and capillary pressure. The diameter of the liquid bridge is usually
small compared to the particle diameter so that the adhesive force due to capillary pressure is
negligible compared to that for surface tension. For completely wetting smooth surfaces, the
adhesive force between a spherical particle and a flat surface is given by
FL = 2 π σ D
(15)
where σ is the surface tension of liquid in contact with air, and D is the particle diameter. The
adhesive force between two spheres of the same diameter is one half of the value calculated from
4
The separation distance is usually not a directly measurable quantity for dusts, and assumptions for its value range
typically from 0.4 to 1.0 nm.
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this equation. Experimental evidence shows that the capillary condensation of water begins to
occur at relative humidity levels above 70 percent.
There are two types of electrostatic forces that may play a role in particle adhesion. The first type
arises from the contact potential, developed between the surfaces of two different materials.
Ranade (1987) states that this type of force increases linearly with particle size, while Zimon
(1982) recommends a two—thirds power dependence on particle size. The second type of
electrostatic force is due to electric charges on the particles or the plate and is called the
Coulomb force. For a spherical particle possessing an electrical charge, Q, resting on a flat
uncharged surface, the Coulomb force is given by
2
Fc =
Q
6(Z + D )
(16)
2
0
where is Z0 the separation distance, and D is the particle diameter. This equation exhibits the
reduction in Coulomb force with increasing particle size if the particle charge were to be
constant. However, particle charge may also depend on the particle size. Dust particles dispersed
by air demonstrate charges increasing slightly less rapidly than the square of the diameter, so that
the Coulomb forces may also increase with the square of the diameter. It should be noted that the
charge on particles contacting a surface will change with time due to electrical leakage. Another
important feature of the Coulomb forces that is different from the other types of adhesion forces
is that they decay relatively slowly with distance, and these forces may play a role even after the
initial dislodgement (e.g., Owen (1969)).
Other types of adhesion mechanisms include magnetism, acid—base interactions (Ranade,
1987), capillary pressure in pore spaces filled with liquid, highly viscous binding agents, and
crystal bridges (Rumpf, 1977).
It is clear from the foregoing discussion that the adhesion theory is far from being a predictive
tool, at this time. The most important conclusion, however, is that adhesive forces are typically
proportional to the particle size. Since the particle weight is proportional to the cube of the
particle size, the forces holding the particle down in a layer is expected to be dominated by the
adhesive force for the small particles, while it is controlled by the particle weight for large
particles. This fact explains the reason why larger particles produce more repeatable and more
predictable results.
For small particles, experimental studies sometimes produced contradictory results. Direct as
well as inverse dependence of adhesive force on particle diameter (or sometimes even complete
independence) has been reported. Zimon (1982) attributed those contradictions to the statistical
nature of adhesive forces. The curves of adhesion number versus adhesion force for different
sizes of the same material are usually not parallel to each other and curiously tend to cross each
other. Depending on the location of the adhesion number taken to characterize adhesion with
respect to cross-over part of the curves, contradictory results will be obtained.
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2.4 Fundamental Studies of Particle Removal from Surfaces
This continues to be an active research area and a large body of experimental and theoretical
work has already been published. A review of the topic can be found in Ziskind et al (1995) and
Gradon (2009). Experiments indicate that adhesion forces as well as the aerodynamic forces
exhibit a stochastic distribution. Coherent structures in the airflow play a significant role on the
threshold entrainment conditions as well as entrainment rates. As a result, entrainment rate is not
constant under specified conditions, but varies as a function of time.
Other experimental variables include underlying surface material, surface roughness, particle
moisture, and the presence of an electrical field. In general, existing theoretical models are
incapable of predicting the experimental data.
Some of the recent noteworthy publications include Ibrahim et al (2008), Jiang et al (2008),
Merrison et al (2007), Grzybowski and Gradon (2005 and 2007), Masuda et al (1994), Gotoh and
Masuda (1998), Hayden et al (2003), Rasmussen et al (2009), Roney and White (2006), Brateen
et al (1990), Friess and Yadigaroglu (2002).
2.5 Applied Research on Aerodynamic Entrainment Threshold
At this point, it should be clear that first principle modeling of aerodynamic entrainment
threshold or entrainment flux does not promise much success due to large gaps in current
capabilities to predict the aerodynamic forces as well as the forces conserving the layer. For that
reason, many studies have been carried out in wind tunnels or in open atmosphere and
correlations have been proposed. While these correlations might be extrapolated to similar flow
conditions and dusts, the major difficulty with this approach is that the results can not be
generalized to all dusts.
Early work of Bagnold (1941) is still the most cited reference of the field. Bagnold studied the
conditions leading to the saltation phenomenon by spreading a thick layer of sand on the bottom
of a 30 x 30 cm cross-section wind tunnel using mean air velocities up to 10 m/s. The sand
particles were typically 100 microns or more in size so that adhesive forces were negligible
compared to particle weight. Bagnold determined that in order to initiate grain movement, the
condition:
τw > 0.01 ρp g D
(17)
must be satisfied. In this equation, τw denotes the wall shear stress5, whereas ρp, D, and g
represent the particle density and diameter and the gravitational acceleration, respectively.
Bagnold also discovered that the saltation, once initiated artificially at shear stresses below the
value of initiation value, can sustain itself so long as:
5
In the literature, three parameters are used commonly to characterize the flow conditions near the wall: wall shear
stress, τw , velocity gradient, γ; and friction velocity, uτ (or u*). These three parameters are uniquely related to
2
2
each other through the following relationship: τw = μ γ = ρ uτ = ρ u∗
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τw > 0.0064 ρp g D
(18)
is satisfied. These equations are often referred to as the static and dynamic thresholds of
saltation, respectively. The reason for the dynamic threshold being lower than the static threshold
was explained by the ejection of new particles from the layer upon impact of saltating particles.
Bagnold observed that the saltating particles leave the surface vertically at a velocity comparable
to the friction velocity of the boundary layer. As discussed earlier, the aerodynamic lift acting on
the particle is too small to explain this behavior. Therefore, the particle ejection is believed to be
due to impact of either rolling or saltating particles. On this basis, however, it is hard to
rationalize the observation that a factor of from two to twenty-five more mass is being conveyed
by jumping than by rolling for various sand and soils (Fuchs (1964)).
Bagnold’s data obtained for sand particles typically larger than 100 um have shown that
smaller particles are moved more easily than larger particles. Numerous experiments performed
later with smaller particles have shown that this trend is reversed for fine particles, so that the
plots of threshold shear stress as a function of particle size have a minimum. The particle size for
minimum threshold shear stress (i.e., for optimum dispersion) has been found to vary with the
type of powder tested and may also be dependent on the details of the experimental conditions.
For example, Zimon (1982) quotes optimal particle sizes of 15-20 um for sylvite dust and 100—
150 um for corrundum particles laying on a steel wall. Similarly, Allen (1970) quotes an optimal
diameter of about 100 um for quartz density sand. The increase of aerodynamic wall shear stress
required to move smaller particles is widely believed to be due to adhesive forces. The adhesive
forces are typically proportional to the particle size, whereas the gravitational force is
proportional to the third power of the particle size, so that the former should dominate the latter
for sufficiently small particles. The aerodynamic forces, reviewed earlier in this section, are
typically proportional to the square of the particle diameter. Therefore, apparent contradiction in
large versus small particle trends are explainable through force-balance theories.
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X
Y
Figure 5. Prediction of a force-balance theory for spherical sand particles in air.
Figure 5 shows the force-balance theory predictions for spherical sand particles (ρp = 2500
kg/m3) in air by Phillips 1980. According to his theory, for large particles, line DE represents the
condition
Aerodynamic drag force = Particle weight
which resulted in τw α D.
For small particles, line XY represents the condition:
Aerodynamic lift = Particle adhesion force
which resulted in τw α D-4/3.
For intermediate size particles, Phillips postulated
Aerodynamic lift = Particle weight
which resulted in threshold shear stress being independent of particle size.
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Numerous studies describing force-balance models and resulting threshold shear stress (or
equivalently threshold friction velocity as defined in footnote 5) curves have been published.
Figure 6. Threshold shear velocity and suspension modes for wind erosion of sand
Figure 6 shows such a curve for threshold shear velocity versus particle size derived for wind
erosion of sand (Greely and Iverson, 1985). Also superimposed on this figure are lines for
constant value of the terminal velocity to friction velocity ratio delineating different modes of
entrained particle motion.
For cohesive dusts, the threshold shear stress (or friction velocity) for particle movement is
recognized to depend strongly on the conditions the deposit has been subjected to since its
formation. For example, for erosion of desert soils, Gilette (1978) recommended actual field
measurements using a portable wind tunnel with an open-floored test section.
A review of the Soviet activity on aerodynamic removal of powders from solid surfaces is given
in Chapter 10 of Zimon (1982). The various experiments described by Zimon include removal of
dust particles by air flow inside long ducts, detachment by a developing flow over a flat plate at
various angles of attack, as well as detachment of particles from cylindrical surfaces by external
air flow. Zimon at times has omitted some of the essential information in his review so that
original papers may have to be referred to before using the data. In an interesting experiment
described by Zimon (1982), spherical glass particles of varying diameter were placed on a steel
plate with a Class IV surface finish6 and were subjected to a 6.2 m/s free stream velocity. The
shear stress on a flat plate decreases with increasing distance from the leading edge; therefore,
close to the leading edge, all the particles are removed, but away from the leading edge none of
the particles are removed. Zimon (1982) used the observed distances for complete removal and
6
This is a Russian designation of surface roughness which corresponds to asperity height of 40 microns (1600
micro-inch).
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no removal to estimate the aerodynamic force required to remove the particles. There are several
drawbacks associated with this type of experiment:
(1) the fact that the boundary layer equations are singular near the leading edge
introduces some uncertainty in calculated flow conditions in this area;
(2) sufficiently away from the leading edge, the boundary layer may display transition to
turbulence which introduces additional uncertainty to the calculated wall shear stresses;
(3) the removed particles transported downstream towards the undisturbed area may have
an effect on the critical distance measured for no particle removal; and
(4) the shear stress, in the laminar flow regime, is inversely proportional to the square
root of the distance from the leading edge, so that a relatively long plate must be used to
observe both distances for complete and no particle removal in a single experiment.
Figure 7. Lift-off apparatus to determine the aerodynamic forces required to remove a dust
deposit
Figure 7 shows the “lift-off” apparatus developed by Ural (1989) to determine the aerodynamic
forces required to remove a dust deposit. Air moves radially inward between the two disks
accelerating towards the center due to the reduction in the effective cross-sectional area. In
addition to radial variation, the local air velocity is controlled by means of changing the gap
between the plates and by adjusting the total airflow rate through the system. Calibration charts
were developed to look up shear stress corresponding to a given radius (of the particle free circle
created by the flow) at a given gap and pressure drop. Figure 8 shows a typical dust removal
pattern which would be considered acceptable for the test method.
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Figure 8. Dust removal pattern in the lift-off apparatus.
Recently, Kalman et al (2005) proposed a general correlation based on particle Reynolds
number, Rep, and the Archimedes number, Ar. The correlation, in the form of three piecewise
continuous equations appear to correlate bulk velocity for pick up threshold, Upu, in gases as well
as in liquids:
Zone I
Zone II
Zone III
Where:
Re*p =
Rep* = 5 Ar3/7
Rep* = 16.7
Rep* = 21.8 Ar*1/3
ρ ⋅ U pu ⋅ d
−
D / D50
1.5
μ ⋅ (1.4 − 0.8 ⋅ e
g ⋅ ρ ⋅ (ρ p − ρ ) ⋅ d 3
Ar =
μ2
(19)
(20)
(21)
(22)
(23)
d: particle diameter
D: pipe diameter
μ: dynamic viscosity
g: gravitational acceleration
ρ: fluid density
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ρp: particle density
Ar* = 0.03 e3.5φ Ar, modified Archimedes number
φ: particle sphericity
A correction factor for non-spherical, relatively large particles was also provided. Figure 9 shows
the goodness of how their correlations match the gas pick-up data, and Figure 10 shows types of
particles used to validate the non-spherical particle correction factor. Figure 11 shows the
threshold (pickup) velocities calculated for spherical glass particles.
Figure 9. Comparison of Kalman et al (2005) correlation with data
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Figure 10. Shapes of non-spherical particles
Figure 11. Comparison of Kalman et al (2005) correlation with data for glass spheres and
other correlations
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2.6 Applied Research on Aerodynamic Entrainment Mass Flux
The measurement of this parameter is significantly more difficult than the entrainment threshold.
Measured values of dust emission by wind erosion typically range from 10-7 to 0.1 g/m2-s,
because of the relatively low velocities experienced in natural winds. Gillette (1977) carried out
indirect measurements of entrainment mass flux for nine different soils as a function of friction
velocity. The large degree of scatter in the data did not permit development of a definitive
correlation. Data seem to support the power relationship between the mass flux Φ and shear
velocity u* through
Φ α u*n
(24)
Where exponent n could range from 3 to 5. Later, Gillette and Passi (1988) suggested a
relationship, which takes threshold entrainment velocity, u*t into account:
Φ = αg u*4 [1 - u*t / u*]
(25)
where αg is a dimensional coefficient. It should be noted that, at high free stream velocities,
boundary layer is affected by the large entrainment mass flux and the exponent n could be as low
as unity.
Hartenbaum (1971) performed a limited number of steady state entrainment tests in a wind
tunnel which had a test section 40” high and 18” wide. Free stream velocities ranged from 34 to
115 m/s. A particulate bed approximately 4” deep at the start of each test was composed of AFS
50-70 Ottawa silica testing sand which had a mean particle diameter of 250 um. The entrainment
rate was correlated to the free stream velocity U with the following equation:
Φ (lb/ft2-s) = 0.366 10-2 [U(ft/s)]5/4
(26)
Hartenbaum also took time to characterize the boundary layer at the test section and fitted a
correlation to the shear velocity:
Φ (lb/ft2-s) = 0.86 10-3 [U*(ft/s)]5/4 – 0.01
(27)
Later, upon request from the US Bureau of Mines, Rosenblatt recast the Hartenbaum’s free
stream velocity equation to include air density effect in an ad hoc fashion. He also included an ad
hoc threshold free stream velocity effect to make the entrainment flux nil at 420 cm/s for mine
applications. The resulting equation:
•
⎡
m" = ρ ⋅ U ⋅ ⎢⎣0.0021 ⋅ U
0.25
−
4⎤
U ⎥⎦
(28)
is still being used by NIOSH for mine research purposes (Edwards and Ford, 1988). Bureau of
Mines measurements (Singer, Harris and Grumer, 1976) indicate that gas-explosion induced air
flow threshold velocities are in the range of 5 to 30 m/s for coal dust. It is noteworthy to point
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out that both Hartenbaum and Bureau of Mines correlations, mass flux is proportional to the 1.25
power of the free stream velocity.
Batt et al. (1995) and Batt et al (1999) reported extensive entrainment data for high-speed air
flow velocities, typically ranging from 100 to 300 ft/s. They developed the following correlation:
ρe ⋅U f ⋅M e0.5
m"=(0.3± 0.1)
α / αWMSR
•
(29)
where:
m”: entrained mass flux
ρe: free stream air density
Uf: friction velocity
Me: free stream flow Mach number
α: angle of repose of soil
αWMSR: angle of repose for soil at the White Sands Missile Range
This equation appears to correlate well the entrainment rate of Ottawa Sand and White Sands
Missile Range soil, over a wide range of parameters tested, and predicts mass flux to be
proportional to the 1.5 power of the free stream velocity. Batt et al (1995) point out that the
larger exponent of 3, proposed originally by Bagnold in 1941, may more appropriate for wind
erosion where the free stream velocity is typically below 20 m/s.
The Batt equation above expresses the mass flux as a function of the friction velocity, Uf. For the
ease of use, it may be preferable to recast equation on the free stream velocity, even at a cost of
precision loss. Since the dust entrainment occurs deep in the boundary layer, friction velocity
rather than the free stream velocity is the more appropriate parameter to correlate the entrainment
rate. On the other hand, most users of the NFPA standards are not anticipated to be versatile in
using aerodynamics concepts encompassing the friction velocity. Therefore, an additional
simplification is introduced by translating the selected entrainment rate correlation to free stream
velocity. The original equation (29) is further modified here for low flow velocities so that
entrainment rate tends to zero at the threshold velocity. Thus, the new equation proposed in this
project is:
⎡ 1/ 2 U t 2 ⎤
m"=(0.002)⋅ρ e ⋅U e ⎢U e − 3 / 2 ⎥
Ue ⎦
⎣
•
(30)
Where, Ue and Ut respectively represent the free stream velocity and the threshold (pickup)
velocity. Equation (30), which constitutes the basis of our new strawman method described in the
next chapter, is an improved version of the NIOSH equation (28), and includes an ad hoc
correction for the appropriate threshold velocity. The coefficient 0.002 of Equation (30) was
selected to envelope the Batt et al data.
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Zydak and Klemens (2007) studied the entrainment rates of dust deposits by airflow. Tests were
conducted in a shock tube / wind tunnel with internal cross section 72 mm by 112 mm. Dust
layer dust thickness tested were 0.1 mm, 0.4 mm or 0.8 mm. The following dimensional
correlation was proposed by these authors:
Φ = 0.004 hl0.216 U1.743 D-0.054
ρp-0.159
Ap0.957
(31)
Where:
Φ: entrained mass flux in kg/m2-s
hl: layer thickness in mm
U: flow velocity above the layer in m/s
D: characteristic particle size um
ρp: particle density in kg/m3, and
Ap: is a dimensional empirical constant.
This is in fact the dust entrainment correlation built into the current version of the DESC code.
Equation 31 assumes that the entrainment mass flux is proportional to the 1.75 power of the free
stream velocity.
The authors selected the following input parameters when developing their correlation:
Sample
Constant Ap
Particle Size D(um)
Coal dust
Potato starch
Potato starch
Silicon dust
1.2
0.745
0.7
1.037
75
35
Particle density
(kg/m3)
1340
1469
1527
2341
Shock tubes have been recognized as a valuable tool in studying aerodynamic dust lift—off
because they provide a well defined flow environment. They also have a direct application in
characterizing the dust lift-off by blast waves emanating from conventional or thermonuclear
explosions. Some examples of this type of experiment performed with non- cohesive dust are
given by Gerrard (1963), Fletcher (1976), Boiko et al (1984), and the references therein. In
interpreting shock tube data, one must be careful about the effect of streamwise compression of
dust layer across the shock wave. This effect often causes a significant lateral dust ejection
velocity and throws the particles beyond the viscous boundary layer.
Fletcher (1976) has subjected layers of treated (free flowing) limestone dust, typically 14 um in
size, to Mach 1.15 to 1.3 incident shock waves. The convective flow velocities under these
conditions vary between 80 and 150 m/s. The dust cloud shapes measured from photographs
were shown to fit the ballistic trajectories of individual particles having an initial vertical
velocity of about 14.5 m/s. Boiko et al (1984) have repeated Fletcher’s experiments with a much
stronger shock (Mach 2.6 corresponding to a convective velocity of 628 m/s). They report
vertical ejection velocities of 40 m/s for 200 um glass particles (ρp = 1200 Kg/m3), and 17 m/s
for 200 um bronze particles (ρp = 8700 Kg/m3).
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The small cohesive particles may be lifted from the surface in the form of aggregates. The
breakdown of these aggregates in a turbulent flow field is of importance in determining the
extent of the dispersion. Singer et al (1976) noted mine dust deposits that have been wetted or
have undergone a wetting-drying cycle may constitute a greater explosion hazard than untreated
dusts owing to selective lifting of relatively large briquetted fragments which then dispersed in
the air stream.
The theoretical progress in the field has been at a rather slow pace. A good physical description
of the various phenomena encountered in the pneumatic transport of non-cohesive powders is
given by Owen (1969).
Corn and Stein (1965) used the calculated particle drag force to interpret their aerodynamic dust
entrainment threshold data. The drag force was calculated using the spherical particle drag
coefficient, and the boundary layer velocity at one particle radius distance from the wall. For less
than 53 um diameter glass beads deposited on glass slide, these authors report that at removal
efficiencies exceeding 75%, the calculated air drag was Within a factor of 2.5 of the adhesion
force measured using the ultracentrifuge method. At lower removal efficiencies, the two forces
differed by as much as a factor of 10. Corn and Stein also report that for the turbulent boundary
layers employed in their experiments, the dust removal efficiency is somewhat dependent on the
test duration. Later, Zimon (1982) repeated these experiments using 20 and 35 um loess7
particles and reported good agreement with the centrifuge method. The formulas used by Corn
and Stein are at best rough estimates of the drag force (parallel to the surface) exerted by air as it
is calculated from the undisturbed velocity in the boundary layer at the level of particle center.
As was stated earlier, the actual drag force for creeping flow was 70 percent higher than that
calculated by the Corn and Stein method. Furthermore, in turbulent flow, some form of a peak
force (rather than mean) should be responsible for particle dislodgement.
Another interesting hypothesis advanced in Zimon’s book was that the maximum diameter of the
adherent particles remaining on a surface after being exposed to a turbulent boundary layer is
equal to the thickness of the laminar sublayer. Zimon suggests the use of this hypothesis as a
means to determine the laminar sublayer thickness. This hypothesis, although demonstrated with
some experiments, is not completely substantiated.
The model of saltation phenomena given by Owen (1964) avoids these fundamental questions on
particle removal using two key phenomenological hypothesis: (1) the effect of the moving grains
on the fluid outside the saltation region is similar to that of solid roughness of height comparable
with the depth of the saltation layer, and (2) the concentration of particles within the saltation
layer is maintained to keep the wall shear stress at the dynamic threshold of Bagnold, given in
Equation (18). These two assumptions are validated by the agreement between the measured and
predicted quantities. Owen (1964) also speculated that the particles would enter into suspension
when the wall shear stress is of the same order of magnitude as ρpgD.
Recently, Mirels (1984) has used Owen’s second hypothesis to calculate the dust erosion rates in
developing turbulent boundary layers over a flat plate and behind a shock wave. Treating the
7
Loess is an unstratified, usually buff to yellowish brown, loamy deposit found in North America, Europe, and Asia
and is believed to be chiefly deposited by the wind.
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effect of dust entrainment on the flow with his previous transpiration model, Mirels reported
agreement Hartenbaum’s high entrainment rate with data within a factor of two. It is remarkable,
if not fortuitous, that Mirel’s simple conceptual model predicted the experimental velocity
exponent very well.
Figure 12 compares the predictions of the several entrainment mass flux equations described in
this section. Calculations were made for 53 micron coal dust particles with a particle density of
1.34 g/cm3. Air density is taken to be 1.2 g/3. Kalman et al (2005) correlation results in a
threshold (pick-up) velocity of 9 m/s for the onset of entrainment. The critical shear stress
needed for the Mirels model was estimated to be 0.15 Pa from the threshold velocity, Equations
(10) and (11) using a friction coefficient of 0.003. The layer thickness needed for the Zydak and
Klemens equation was assumed to be 1/32”.
Entrained Mass Flux m" (kg/m2-s)
10
Mirels
Batt et al
Zydak & Klemens
NIOSH
This Work, Eq. (30)
Error Bounds
1
0.1
0.01
0.001
1
10
100
Free Stream Velocity Ue (m/s)
Figure 12. Comparison of the predictions from various entrainment mass flux equations
for 53 micron coal dust.
All equations seem to agree with each other within a factor of three for the high speed flows. The
disparity for low speeds were not unexpected since the NIOSH equation was forced to predict
zero entrainment at 4.2 m/s, whereas Batt et al, and Zydak and Klemens correlation tend to no
entrainment only when the free stream velocity approaches zero.
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2.7 Secondary Explosion Propagation Tests
In these experiments combustible dust deposited on the floor of a gallery is dispersed and ignited
by a primary explosion at the beginning of the gallery. Measurements typically include pressure
development, apparent flame speeds, and gas velocities. Examples of these types of experiments
can be found in Tamanini (1983), Richmond and Liebman (1974), and Michelis et al (1987).
These experiments are quite costly, and therefore have been performed using very few types of
dusts (mostly coal dust, and some cornstarch). Since a number of phenomena play crucial roles
in sequence in these experiments, the results are often not repeatable. In order to improve the
repeatability problems, the tests are designed so that the secondary explosion is overdriven by a
strong primary explosion.
Similar tests have been carried out at intermediate scale. Tamanini (1983) used a 6 m long model
gallery with 0.3 m2 cross-section to study secondary explosions of cornstarch. Recently, Srinath
et al (1987) tested a number of dusts in their 0.3 m I.D. 37 m long flame acceleration tube. The
scaling of test results from intermediate scale to actual size galleries should be difficult, at best.
Investigations aimed at understanding the aerodynamic dust entrainment in mine galleries have
been carried out at the U.S. Bureau of Mines, as an extension of the early British work (Dawes,
1952).
Singer et al (1969) measured the minimum air velocities required for dispersal of coal and rock
dust deposited at the floor of a small wind tunnel test section (7.62 cm wide, 2.54 to 5.08 cm
high). Tests have been carried out using monolayer dust deposits, as well as piles of dust. The
effects of type of surface holding the dust, relative humidity of the dust pre- conditioning
atmosphere, and the large-amplitude oscillations superimposed on the air stream on the threshold
dust entrainment velocity were studied. The air flow rate was transient during the tests, with a
reported rise time of 1 minute.
In the monolayer studies, the average air velocities required to remove 25, 50 and 75 percent of
the particles (by microscopic number count) were determined. The measured threshold velocities
for 75% dust removal ranged from 20 to 130 m/s, increasing with decreasing particle size. The
calculated wall shear stresses in this configuration range from 1 to 30 Pa. The measured
threshold entrainment velocities for the three types of dust tested increased in the order: rock
dust, anthracite, and Pittsburgh seam coal. The differences in the threshold velocities of these
dusts diminished for particle sizes below 10 um. The rock dust was removed more easily from
smooth Pittsburgh seam coal and glass surfaces than from smooth anthracite.
In tests with dust piles, the minimum air velocity required for complete removal of the dust pile
was measured. Velocity measurements were taken upstream of the pile, at a distance from the
tunnel floor equal to mid-height of the ridge. The types of dust removal observed included
erosion, denudation, as well as removal of massive clumps and sliding of the entire ridge. The
reported threshold velocities spanned the range from 5 to 23 m/s. It was found that the
compaction of ridge significantly increases the threshold entrainment velocity, whereas the
presence of vibrations either in the air flow or on the floor reduces it. The relative humidity of
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dust in the range of 35 to 90 percent was found to have no significant effect on the threshold
velocity. Interestingly, for the dust piles tested, anthracite dust was easiest to be removed, while
rock dust was the most difficult, an order different than observed for monolayers.
Singer et al (1972) have later attempted to relate the entrainment threshold of dust piles to the
shear cell data believed to be some representation of the cohesive forces between the particles.
First, they have defined a threshold Froude number:
Fr =
τw
ρb gτ y H / 2
where:
τw aerodynamic wall shear stress;
τy shear cell yield stress extrapolated to no load;
ρb bulk density of powder;
g gravitational acceleration; and
H height of the dust piles.
The denominator was stated to be the “geometric mean of the gravitational and cohesive forces,”
yet it lacks any physical significance. Singer et al (1972) found that for their limited number of
data points, this Froude number remained relatively constant within the range 0.0077 to 0.038 for
their dust ridges and beds. These authors also tried the ratio of the aerodynamic dynamic
pressure at the mid-height of the pile to Ty and found it to cover the range between 0.22 and
0.75.
A limited number of threshold tests were repeated in a large scale (1.5 m high, and 2.4 m wide)
wind tunnel, which indicated that the threshold velocities in the large scale wind tunnel is a
factor of 1 to 3 smaller than those measured in the small wind tunnel. These authors have also
made some entrainment rate measurements and presented their results as data correlations. These
correlations must be used with extreme caution beyond their intended range or for different dusts
because they are not based on physical reasoning.
In a follow-up, work Singer et al (1976) have used actual explosion induced air flow, fraction of
a second in duration, to study the dust dispersion phenomena. Most tests were carried out in a
0.61 m I.D. 49.7 m long explosion tunnel, while some tests were repeated in the full scale
experimental mine gallery. The instantaneous threshold air velocities in these explosion tests
were found to be in the same range as the earlier slow-rise threshold velocity tests described
above. One of the important objectives of this study was to study the selective dispersion of coal
dust over rock dust, which would decrease the inerting probability. It was found that the
uniformly mixed beds always dispersed without separation, whereas in the case of coal dust layer
deposited over a rock dust layer, only the coal dust is dispersed if the peak airflow velocity is in a
range between the threshold velocities of the two dusts.
Hwang et al (1974) modeled the dispersion phenomena using the diffusion equation. The details
of the entrainment were completely ignored and the entrainment rate, specified as a denudation
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rate, was left as input. This model also ignores the effects of gravity. There is also a great
uncertainty in picking a diffusion coefficient which was stated to be between 0.2 to 362 cm2/s.
These authors recommended the use of diffusion coefficients in the range 25 to 100 cm2/s as
“best guess,” which results in a factor of four variation in the calculated dust concentration.
The modeling effort at the University of Michigan was focused on the coupling of the dust liftoff with flame propagation. In this model, the one-dimensional flame propagation model of Chi
and Perlee (1974) was mated with the entrainment rate model of Mirel (1984) described above.
The agreement with the data given in Srinath et al (1987) was qualitative. The limitations of this
approach arose from the fact that the mixing process and the effects of gravity were not included.
More recently, Li et al (2005) examined the possibility of deflagration to detonation transition
supported by layers of corn dust, cornstarch, Mira Gel starch, wheat dust, and wood flour. Flame
speeds of up to 1300 m/s were observed, which the authors called quasi-detonations.
2.8 Computational Simulation of Aerodynamic Dust Entrainment Phenomena
Computational Fluid Dynamics (CFD) tools have also been used to predict the entrainment
phenomena. Iimura et al (2009) studied the removal agglomerates by shear flow, using a
modified discrete element method. Ilea et al, in University of Bergen developed an EulerianLagrangian model and studied various aspects of dust entrainment behind a shock wave.
Dust Explosion Simulation Code (DESC) is a CFD models sometimes used to simulate
secondary explosions. However, as was discussed above, these models rely on very crude
correlations to represent the entrained mass flux. Hence, it is hoped that the CFD models too will
benefit from this project.
2.9 Gaps in Available Information
This study revealed serious gaps in the available information.
Even though a large body of fundamental experimental and theoretical work has already been
published, existing theoretical models are incapable of predicting the experimental data. This
difficulty is inherent in the phenomena involved in dust entrainment, as experiments indicate that
adhesion forces as well as the aerodynamic forces exhibit a stochastic distribution. Coherent
structures in the airflow play a significant role on the threshold entrainment conditions as well as
entrainment rates. As a result, entrainment rate is not constant under specified conditions, but
varies as a function of time. Additionally, factors such as underlying surface material, surface
roughness, particle moisture, and the presence of an electrical field also display significant
effects.
Applied research focused on specific applications thus resulting in more encouraging predictive
tools. There exist a significant number of publications, which can be distributed into clusters
such as atmospheric erosion, pneumatic transport, fluidization, pharmaceutical delivery,
atmospheric emission. Unfortunately, due to limitations in applicability, these studies are not
directly useable for the present project.
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There exist a limited number of experimental studies secondary explosions. However, scale,
geometry and the parameters of these tests limit their generalization to the broad range of
industrial applications.
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III
Proposed Strawman Method
3.1 An introduction to the Proposed Strawman Methodology
Recently, the Committee responsible for NFPA 654 came up with two new consensus criteria for
determining that a compartment is a dust explosion hazard: one aimed at mitigation of burn
injuries, and the other for room/building collapse prevention. As described in Rodgers and Ural
(2010), the criteria are based on maximum allowable airborne combustible dust mass. Both
formulas rely on an empirical entrainment fraction, ηD, representing the fraction of dust
accumulations that can become airborne during an accident. After much discussion, the
Committee selected a value of ηD = 0.25 which offers the same level of protection NFPA 6542006 does for typical occupancies, pending the outcome of this Research Foundation sponsored
project.
The objective of the method is to estimate the amount of dust that can be removed from dust
layers by a primary event such as a pressure vessel burst or a primary explosion, thus eliminating
the need to use an empirical value for entrainment coefficient. The prediction will obviously
depend on the nature and the strength of the primary event, the air velocity it induces over the
layer as a function of location and time, and the resistance of the dust in the layer against
entrainment.
Mathematically, if a primary event is capable of inducing velocity u=u(x,y,t) over the layer, and
the entrainment mass flux for the particular dust is given by the expression m” = m”(u), then the
total mass of dust removed from the layer, M, can be expressed as:
M = ∫ ∫ ∫ m"[u ( x, y, t )] ⋅ dx ⋅ dy ⋅ dt
(32)
Since such a rigorous approach is impractical for the anticipated end users, a simplified approach
was sought. The simplification was achieved by narrowing down the initiating events to a few
typical primary event scenarios. Additional simplification was achieved by breaking the
methodology into several components and further simplifying them. These components include:
• Estimation of threshold entrainment velocity for dust
• Estimation of entrained mass flux
• Estimation of the flow velocity and duration induced by the primary event
• Estimation of total entrained mass
While this approach can result in some loss of generality and precision, its ease of use is
obviously a major benefit.
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3.2 Estimation of Threshold Entrainment Velocity for Dust
Empirical algebraic relationships proposed by Kalman et al (2005) were selected for use in this
phase of the project. Three expressions were provided for different particle size groups,
accounting for particle size and particle density. An additional equation was provided to account
for the particle shape for the large particle regime.
Spherical Particles
Threshold Velocity (m/s)
30
Wood (0.5 g/cm3)
25
Sugar (1.5 g/cm3)
Aluminum (2.7 g/cm3)
20
Iron (7.8 g/cm3)
15
10
5
0
0
100
200
300
400
500
Particle Size (microns)
Figure 13. Calculated threshold entrainment velocity as a function of particle size and
particle density
The end users of this methodology are expected to refer to a chart similar to that shown in Figure
13, which was created using the Kalman et al equations. For example, if the particular dust were
made up of atomized aluminum particles of 100-micron diameter, then no entrainment would be
expected so long as the free stream velocity, Ut, over the layer is below 7.5 m/s, as read from
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Figure 13. Alternatively, the minimum value of the appropriate curve can be used for polydisperse dusts (i.e. dusts made up of particles with a broad size range). For nearly spherical
particles, the minimum threshold velocity (in m/s) is:
Ut = 0.46 ρp1/3
(33)
and it corresponds to the optimal particle size (in meters):
Dopt = 7.9 * 10-4 ρp-1/3
Where ρp is the particle density in kg/m3. Variation of the minimum threshold velocity and the
corresponding optimal particle size with particle density is charted in Figure 14. In applications
where dust particles are expected to be removed as agglomerates, substituting particle density
with bulk density may be more appropriate. Non-spherical particle shapes are treated using a
correction factor based on the particle sphericity.
The end users of this methodology are expected to refer to a chart similar to that shown in Figure
1, which was created using the equations provided in Kalman et al (2005). For example, if the
particular dust were made up of atomized aluminum particles of 100-micron diameter, then no
entrainment would be expected so long as the free stream velocity, Ut, over the layer is below 7.5
m/s, as read from Figure 13. Alternatively, if the Aluminum sample is poly-disperse, then
Equation (33) or Figure 14 gives Ut = 6.4 m/s for particle density of 2700 kg/m3.
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140
Threshold Velocity
Threshold Velocity (m/s)
12
120
Particle Size
10
100
8
80
6
60
4
40
2
20
0
0
3,000
6,000
9,000
12,000
Optimal Particle Size (microns)
14
0
15,000
Particle Density (Kg/m3)
Figure 14. Variation of the minimum threshold velocity and the corresponding optimal
particle size with particle density for nearly spherical particles.
3.3 Estimation of the entrained mass flux
Inspired by the literature reviewed in the first task of this project, the following equation was
selected to estimate the entrainment mass flux8:
m” = 0.002*ρ*U*(U1/2 - Ut2 / U3/2)
U > Ut
(30)
where:
m” entrained mass flux in kg/m2-s
ρ gas density in kg/m3
U free stream velocity (i.e. velocity outside the boundary layer) in m/s
Ut threshold velocity in m/s determined from Figure 13 or Equation (33).
8
The rate of mass removal per unit area per unit time.
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This equation predicts that the entrainment mass flux is proportional to the 1.5 power of the free
stream velocity and goes to zero when the free stream velocity approaches the threshold velocity.
3.4 Comparisons with Large Scale Explosion Data
The Equations (30) and (33) represent the essence of the new strawman methodology. Their
predictions are compared to the available test data in this section.
NIOSH TESTS: The National Institute for Occupational Safety and Health (NIOSH), Office of
Mine Safety and Health Research (OMSHR) has conducted large-scale dust explosion tests in an
experimental mine (Cashdollar et. al, 2010). The gallery is approximately 1600 ft long, 7 ft high
and 20 ft wide. Before each test, the gallery was thoroughly washed down. Dehumidified air was
passed through the gallery, and the gallery was allowed to dry several days before dust was
loaded. As seen in Figure 15, tests were driven by the ignition of a methane air mixture.
Typically, the first 40-ft (12 m) section of the mine gallery, starting at the face (closed end) was
filled with 10% methane in air mixture. A plastic diaphragm was used to contain the methane-air
mixture within the flammable gas mixture zone before ignition. The coal dust and limestone rock
dust mixture was placed half on roof shelves made of expanded polystyrene and half on the floor
as illustrated in Figure 15. These roof shelves were suspended 1.5 ft (0.5 m) from the mine roof
on 10-ft (3 m) increments throughout the dust zone which was 300-ft long (i.e. spanned the 40 ft
to 340 ft distance from the face. The roof shelves were often damaged during the deflagration,
and resulting debris occasionally landed on the test bed causing easily identifiable gouges on its
surface. The amount of the dust mixture placed in the dust zone corresponds to a nominal dust
loading9 of 200 g/m3. Ignition of the methane-air mixture alone would result in flame travel up
to approximately 200 ft from the closed end. The methane air zone was ignited near the center of
the face using electric matches grouped in a single-point configuration.
9
The nominal dust loading assumes that all of the dust was dispersed uniformly throughout the cross-section.
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Figure 15. Experimental setup in NIOSH tests. Top: Side view schematics of the mine
geometry, Left: Placing Coal/Rock dust mixtures on the shelves, Right: distributing dust on
the floor (from Cashdollar et al, 2010).
Based on personal communications with Marcia Harris, a Research Engineer with OMSHR, the
dust removal experiments within the NIOSH experimental mine were setup and conducted in the
following manner (Harris et. al, 2009). The dust bed for the dust removal tests (Figure 16) was
prepared at a location 250 ft (to 258 ft) from the face (ignition end) between two aluminum rails.
These rails were 1-inch high by 100-inches long, parallel to the gallery axis, and attached to the
mine floor 22-inches apart. The dust was placed between the rails and leveled; creating a 1-inch
deep layer. Before and after the explosion test, the dust layer depth was measured, to within ±
0.1 mm accuracy, at stations 24”, 36”, 48”, 60”, 72”, 84” and 96”. The depth change at each
station was attributed to the dust removal due to explosion. Time resolved gas flow velocity
induced by the primary explosion near the dust bed was also recorded using a bi-directional
velocity probe located few feet downstream of the bed near the center of the mine cross-section.
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Figure 16. Measuring the amount of dust scoured during an explosion
(from Harris et al, 2009).
Figure 17 shows the velocity recorded near the dust bed (containing a 35% coal dust 65% rock
dust mixture) in experimental mine test 511. The dust removal depth shown in this figure was
calculated from the new strawman method. Equation (33) estimates the dust bed threshold
velocity, Ut, to be 6.4 m/s10. Inserting the instantaneous gas velocity and gas density into
Equation (30), dust removal rate (entrainment mass flux) is calculated as a function of time.
Cumulative mass removal per unit area (kg/m2) is calculated as a function of time by integrating
entrainment mass flux over time. Dust bed bulk density of 850 kg/m3 was used to convert the
cumulative mass removal to dust removal depth shown in Figure 17. Our strawman methodology
is seen to predict that the particular explosion created in this test will remove approximately top
2.4 mm of the 25 mm thick dust bed, corresponding to a 9% entrainment fraction. Dust removal
observed in the test ranged from 1 mm to 2.5 mm depending on the location along the bed
(Figure 6).
10
The particle densities for the coal dust and rock dust are 1330 and 2750 kg/m3, respectively. Since tested mixtures
were mostly rock dust (64 to 80% rock dust by weight), rock dust particle density was used to estimate the threshold
velocity.
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200
2.4
160
2
Gas Velocity
(measured)
Dust Removal
(predicted)
120
1.6
80
1.2
40
0.8
0
0.4
-40
Dust Removal (mm)
Gas Velocity (m/s)
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0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Time (s)
Figure 17. Gas velocity recorded near the dust bed during the experimental mine test 511,
and the corresponding dust removal depth calculated from Equation (30).
Figure 18 shows the experimental dust removal depths determined from pre and post explosion
depth measurements (Harris, 2010). Table I lists the key results obtained in all NIOSH tests
conducted in this particular program. Measured dust removal depths reported in the sixth column
represents the average of the depth changes observed in stations 36”, 48”, 60”, 72”, and 84”. The
removal data from the first and last stations were ignored due to potential edge effects. The last
column of Table I shows the predictions of the new Strawman method, calculated from the
velocity data as described above. The strawman methodology is seen to provide a reasonable
representation of the data.
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3.0
Dust Removal (mm)
2.5
2.0
1.5
1.0
Experiment
Strawman
0.5
0.0
0
12
24
36
48
60
72
84
96
Distance along Bed (in)
Figure 18. Experimental mine and theoretical dust removal depths for test 511.
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Table I. Key NIOSH Results
Test No.Test Bed
Location
498-125ft
498-320ft
499-125ft
499-227ft
499-320ft
511-250ft
512-250ft
513-250ft
514-250ft
516-250ft
517-250ft
518-250ft
520-250ft
% Rock
Dust in
Coal Dust
%
80
80
65
65
65
65
75
80
64
69
71.7
74.4
68.5
Coal Dust
type in
Mixture
PPC
PPC
PPC
PPC
PPC
PPC
PPC
PPC
Coarse
Coarse
Medium
Medium
Medium
Pressure Data
Dynamic
Dynamic
Pressure
Pressure
Peak
Impulse11
psi
psi-sec
18.9
0.4
3.3
0.3
2.6
0.4
5.4
0.5
9.7
0.2
7.1
0.9
1.3
0.3
1.1
0.3
6.4
0.8
4.8
0.6
3.8
0.5
4.2
0.5
6.0
0.7
Dust Removal
Strawman
Measured
Method
Prediction
mm
mm
1.0
1.1
1.2
1.0
2.1
1.1
1.6
1.5
2.1
1.5
2.0
2.4
2.6
1.3
1.0
1.0
2.1
2.1
1.2
1.8
1.6
1.6
2.1
1.5
1.4
2.2
Notes: PPC denotes Pittsburgh Pulverized Coal that contains 80% fines that go through 200
mesh (74 microns). Medium and Coarse Coal Dust respectively contain 40 and 20% fines that go
through 200 mesh. The tests 498 and 499 each employed a 70 ft long gas ignition zone and the
dust beds were placed at 125, 227 and 320 ft distance from the face.
B. NGFA TESTS:Another large-scale explosion study, where the quantity of dust removal was
carefully measured, was reported by Tamanini (1983). The tests were conducted in an 8’ by 8’
by 80 feet long gallery connected at one end to a 2250 ft3 chamber. The other end of the gallery
was open to atmosphere. Before each test, a uniform layer of cornstarch was laid on the gallery
floor using a modified lawn spreader. After each test, the gallery was swept and the dust residue
was collected and weighed. Primary explosion was created by igniting a cornstarch cloud
(nominally 125 g/m3) formed in the primary chamber. The table below, taken from Tamanini
1983, lists the tests performed, the amount of cornstarch spread over the gallery floor (first
column), and the amount of cornstarch picked up (second column) by the explosion, reported as
a corresponding average concentration in the gallery.
11
Dynamic pressure impulse is the integral of dynamic pressure over time.
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The concentrations reported in the first two columns can be converted into layer densities by
multiplying them by the gallery height of 8 ft, or 2.4 m. For example, for the last test in the table
(NGFA56), 227 g/m2 (i.e. 93 g/m3 X 2.4 m) cornstarch was spread over the floor, and explosion
removed 119 g/m2, corresponding to an entrainment fraction of 53%.
Tamanini measured the pressure development in the primary chamber as well as at four different
stations along the gallery. The data from test NGFA56 is shown in Figure 19. An examination of
this pressure data reveals the following:
- There are no significant differences among the primary pressure pulses experienced
in the primary chamber and at upstream stations in the gallery,
- Primary pressure pulse travels downstream at approximately sound speed, and
- The period of the Helmholtz oscillations are substantially smaller than the period of
the primary pulse.
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0.5 s
1.0 s
1.5 s
Figure 19. Pressure data from test NGFA56.
These observations suggest that the free stream gas velocity in the gallery might be estimated
using the acoustic approximation for a simple wave defined by the measured pressure pulse. The
red curve superimposed, in Figure 19, on the pressure trace recorded at 8.0 m in the tunnel
represents our approximation to the time resolved pressure data in the gallery. For cornstarch,
Equation 33 predicts a threshold velocity of 5.3 m/s. Resulting entrainment predictions are
compared to the test data in Figure 20. The abscissa in Figure 20 corresponds to the peak
pressure Tamanini recorded at the 8 m station. Considering the uncertainty due to gas velocity
estimation, the agreement between the data and predictions is encouraging.
Towards Estimating Entrainment Fraction for Dust Layers
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Dust Pickup Concentration (g/m3)
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100
80
NGFA Data
60
Strawman Method
40
20
0
0
0.5
1
1.5
2
Peak Pressure at 8 m (psig)
Figure 20. Comparison of the cornstarch entrainment predictions with NGFA data.
3.5 Estimation of the dust entrainment caused by primary event scenarios
Previous section showed that when the free stream velocity near the dust layer is known as a
function of time, the new strawman method provides a reasonable representation of the dust
removal data. When applying the strawman method for industrial hazard evaluation, temporal
and spatial variation of the free stream velocity over the dust layer needs to be considered. This
can be done with detailed computer modeling or using a simplified approach.
To demonstrate the latter approach, Project Panel task group selected the following typical
examples:
Example A: Catastrophic burst of an indoor equipment (e.g. dust collector), and
Example B: Dust deflagration venting from a room into another room.
The dust entrainment in scenario A is driven by a blast wave, while that in Scenario B is driven
by the vent discharge flow.
EXAMPLE A: Catastrophic burst of an indoor equipment
Consider a 74 ft3 dust collector sitting on the floor, in the middle of a plant bursts at 0.5 barg.
The floor of the plant is covered with a thick layer of aluminum dust made up of 100 micron
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spherical particles. In this scenario, the Baker-Strehlow method12 for bursting spheres can be
used. If the burst is caused by an internal deflagration, the average temperature inside the
enclosure depends on the availability of venting prior to burst. In this analysis, the enclosure
contents were assumed to be at the ambient temperature and have the specific heat ratio of 1.4
prior to the burst, since this produces results that are more conservative. Effects of any
combustion or shock wave reflections after the burst are ignored. For the burst pressure of 0.5
barg, Baker-Strehlow method predicts a maximum side-on pressure of 0.22 barg at the burst
surface, approximately one-half of the burst pressure.
Since the dust collector is sitting on the floor, we can approximate the geometry as a hemisphere
as shown in Figure 21. The hemispherical treatment accounts for the confinement of the blast
wave due to floor by doubling the dust collector volume, but ignores effects such as oblique and
mach reflections. For the dust collector volume of 74 ft3, then the hemisphere radius is 1 m.
Figure 22 shows the peak pressure field predicted by the Baker-Strehlow method. The peak
velocity field is ideally calculated using the shock relations. However, since the peak pressures
are low, acoustic approximation is adequate in this case:
U=
ΔP
ρ ⋅a
(34)
Where:
U=U(r): peak free stream velocity (m/s) at radius r
ΔP=ΔP(r): peak pressure rise (Pa) at radius r
ρ: density of air (1.2 kg/m3), and
a=340 m/s speed of sound in air.
The peak velocity field calculated using the acoustic approximation is also shown in Figure 22.
The peak velocity is seen to be equal to the 7.5 m/s threshold velocity, for the 100-micron
Aluminum dust example above, at a radius of 5.6 meters. Therefore, beyond the 5.6 m “threshold
radius13”, our methodology predicts no entrainment. Peak velocity never exceed 54 m/s, a value
determined strictly by the burst pressure.
Figure 23 shows the local peak entrainment flux calculated using Equation (30).
At a given location, both the overpressure and velocity suddenly jump from zero to their
respective peak values, and start decaying exponentially. After a finite period both the
overpressure and velocity go through zero and change sign. For the sake of simplicity here, we
will assume the peak overpressure and velocity at a given radius remain constant for a finite
period. Its duration can be estimated from the peak overpressure and impulse values predicted by
the Baker-Strehlow model. Assuming a triangular waveform:
Duration, Δt = 2* Impulse / (Peak Overpressure)
(35)
12
See, for example, CCPS (2010) for a calculation procedure.
The threshold radius scales with the cube root of the bursting enclosure volume, and can conceivably be utilized
to establish safe separation distances.
13
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Figure 21. Hemispherical vessel burst in the middle of the plant.
Peak Pressure (psi) or Velocity (m/s)
100
10
Peak Pressure
Peak Velocity
1
0.1
1
10
Radius from Center (m)
Figure 22. Peak pressure and velocity fields created by a 74 ft3 hemispherical enclosure
burst at 0.5 bar pressure.
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It should be pointed out that this is a very conservative assumption for the dust entrainment
calculations. For the present example, a duration Δt = 0.0028 sec is predicted.
Figure 24 shows the local entrained mass per unit area for the 100-micron Aluminum dust, and is
calculated by multiplying the flux shown in Figure 8 with the 0.0028 second duration.
Total entrained mass is calculated by integrating the values shown in Figure 24 over the radius
and is calculated to be only 19 grams. In other words, the new strawman methodology predicts
no secondary explosion hazard for this scenario.
Peak Entrained Mass Flux (kg/m2-s)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1
10
Radius from Center (m)
Figure 23. Local peak entrainment mass flux for the 100-micron Aluminum dust
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Entrained Mass density (kg/m2)
0.004
0.003
0.002
0.001
0
1
10
Radius from Center (m)
Figure 24. Local entrained mass per unit area for the 100-micron Aluminum dust
EXAMPLE B: Dust deflagration venting from a room into another room
Consider a 100 m3 primary enclosure communicating with the rest of the building through a 6’
by 8’ opening. The floor of the building is covered with a thick layer of aluminum dust made up
of 100 micron spherical particles. In this example, we will estimate how much dust can become
airborne if a 1 psi (6895 Pa) overpressure deflagration occurs in the primary enclosure.
For the sake of simplicity and conservative results, vent discharge is treated as a quasi-steady14
turbulent round momentum jet, hugging the floor at the jet axis. A conceptual sketch is provided
in Figure 25. Since the vent opening is adjacent to the floor, the discharge jet takes the form of
one-half of an axial jet discharging from an outlet twice as large. Air entrainment occurs almost
exclusively along the surface of a half cone, and the maximum velocity remains close to the
surface. Effects of surfaces other than the floor are ignored. Flame is assumed to exit the primary
explosion enclosure after all the contents have been consumed. This is a conservative assumption
consistent with rear ignition.
14
Temporal evolution process of the vent discharge jet was not considered to keep the analysis simple for the end
user.
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Vent
Wall
Imaginary
Vent
Floor
Figure 25. Conceptual schematics of vent discharge treated as half a round floor jet
The peak discharge velocity can be calculated from the Bernoulli’s equation. For the most
conservative discharge coefficient of unity, exit velocity is
Uo =
2 ⋅ ΔP
ρ
=
2 ⋅ 6895
= 107 ⋅ m / s
1.2
(36)
The opening has a cross-sectional area of 48 ft2 or 4.5 m2. To simulate the effect of the floor, a
mirror image imaginary vent below the floor is considered and the discharge area is doubled.
Therefore, equivalent discharge diameter, Do is 3.37 meters.
Variation of the peak axial velocity in a free jet is approximately represented with four zones
(see, for example, ASHRAE 2005). Zone 1 is a short core, extending several exit diameters, in
which the maximum velocity of the flow remains practically unchanged. Zone 3 represents fully
established turbulent flow that may be 25 to 100 diameters long. Transitioning between Zones 1
and 3, there is a short Zone 2. Zone 4 is a zone of jet degradation where the flow velocity
becomes comparable to that for preexisting turbulent fluctuations and convective currents.
In this example, peak axial velocity decay with axial distance X is represented by the equation:
U = Uo min[1, 6.2 D/X]
(37)
It should be noted that Equation (37) represents Zones 1 and 3, while ignoring Zones 2 and 4.
If we assume a top-hat velocity profile, the width, W, of the jet hugging the floor at distance X
has to be
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W = Do Uo / U
(38)
to preserve the momentum.
Assuming all vent discharge occurs at the 107 m/s exit velocity, the discharge duration is limited
with the mixture in the primary enclosure, and can be calculated as:
Δt =
7
100m3
⋅
= 0.18 sec onds
8 4.5m 2 ⋅ 107m / s
(39)
if there are no other vents available for discharge. The factor 7/8 accounts for the residual burnt
mixture inside the primary enclosure. The discharge duration is controlled by the volume of the
primary enclosure. Alternatively, Equation 6.3.5.5. in NFPA 68 predicts a discharge duration of
1.0 seconds for Pmax = 8 barg.
Figure 26 shows the peak velocity as a function of distance from the vent opening. The
magnitude of the maximum velocity is 107 m/s and is determined by the pressure the primary
deflagration enclosure can withstand. The velocity decay with distance is seen to be slower in
this Scenario, owing primarily to the directionality of the discharge. The velocity decay is
controlled by the area of the vent opening. However, unlike the burst scenario which sends a
blast wave in all directions, the vent discharge affects dust layers only over a narrow path of
width W along the jet axis.
Figure 27 is a plot of the local peak entrainment flux calculated using Equation (33).
Figure 28 shows the local entrained mass per unit area for the example worked out in this
section, and is calculated by multiplying the flux shown in Figure 12 with the 0.18 second
duration. It is instructive to note that the simplified analysis presented here predict, for the
worked out example, entrainment of 0.5 kg/m2 at the vent opening, and 0.13 kg/m2 at 50 m
distance from it. Recognizing the fact that layer thickness allowance in current NFPA standards
work out to be approximately 1 kg/m2, method predictions correspond to entrainment fraction of
to 50% at the vent opening, and 13% at a distance of 20 meters, for the threshold layer
thicknesses. Predicted entrainment fraction is less for thicker layers.
The simplified equations presented here predict entrainment for distances up to 300 m, and result
in a total entrained mass of 173 kg. In reality, the length of the discharge jet is limited either
because it impinges on a wall, or because it detaches from the floor due to buoyancy. To estimate
the latter effect, flame projection distance given by Equation 8.8.2 of NFPA 68 may be used. For
a 100 m3 room, single vent, and a K coefficient of 10 for metal dusts, a flame projection distance
of 46.4 m is calculated. The Strawman method results in a total entrained mass of 68 kg up to
46.4 m distance.
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12
100
10
Peak Velocity (m/s)
120
80
8
Peak Velocity
Discharge Width (m)
60
6
40
4
20
2
0
0
0
10
20
30
40
Discharge Width (m)
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50
Distance from the Door (m)
Figure 26. Peak velocity field, and the discharge width created by the Example worked out
for Scenario B.
Peak Entrained Mass Flux (kg/m2-s)
3
2.5
2
1.5
1
0.5
0
0
10
20
30
40
50
Distance from the Door (m)
Figure 27. Local peak entrainment mass flux for the Example worked out for Scenario B.
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Entrained Mass density (kg/m2)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
Distance from the Door (m)
Figure 28. Local entrained mass per unit area for the Example worked out for Scenario B.
3.6 Extension of the Strawman Method to Elevated Surfaces
The data used to develop Equation (30) were obtained in experiments with airflow over dust
deposits covering relatively large surface areas. Equation (30) should also be applicable to dust
deposits with streamwise dimension exceeding 2 m long. However, most elevated surfaces such
as typical I-beams and roof support structures have characteristic dimensions that are
substantially smaller than 2 meters.
The work of Batt et al (1995), Equation (30) is partly based upon, determined that dust
entrainment flux is proportional to the inverse square root of the dust deposit length. Even
though such a behavior is not evident in the NIOSH data, inverse square root dependence rule
may be used to extend the strawman method to deposits on elevated surfaces, until validation
tests are performed.
This can be implemented easily by calculating a multiplication factor α for entrained mass flux:
α=
2
L
for L < 2m
(40)
Where L is the streamwise dimension of the elevated surface in meters.
As an example, consider the dust deposit on a 4” (0.1 m) wide I-beam placed in the near field of
the deflagration vent discharge in Example B, above. Then entrainment mass flux from the I-
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beam can be calculated by multiplying Equation (30) with the factor factor α = 4.5. Since earlier
calculations based on Equation (30) showed that dust entrainment from floor deposits is
approximately 0.5 kg/m2, the dust entrainment from the I-beam will be approximately 2.25
kg/m2. Primary deflagration will remove top 2.25 mm of the dust deposit on the I-beam, if the
bulk density of the dust deposit is 1000 kg/m3. This corresponds to an entrainment fraction of
71% if the dust layer thickness is 1/8”, or 100% if the dust layer thickness is smaller than or
equal to 2.25 mm.
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IV
Validation Plan
As discussed in the previous chapter, the new strawman method is essentially comprised of two
major components:
a. selection of the types, magnitudes and durations of the maximum credible disturbances
b. calculation of the mass of the dust entrained from the deposits.
The first component depends on the primary event scenarios that are credible for the specific
occupancy. The two most commonly encountered scenarios have been developed in the previous
chapter. It is anticipated that additional scenarios will be identified and developed as the new
strawman method is being adopted into the combustible dust occupancy standards. When
developing the two scenarios presented in this report, it was possible to identify and utilize wellknown simple tools. The same may be true for the new scenarios as well.
The heart of the strawman method is the entrainment mass flux correlation. Even though it was
predominantly based on high quality data, additional tests will be useful to build confidence on
its applicability to a wide range of combustible dusts covered in NFPA 61, NFPA 484, NFPA
654, and NFPA 664. Depending on how well the correlation compares to the new data, its
coefficient and exponents may be adjusted as necessary.
4.1 Uncertainties in the mass flux correlation
The high velocity portion of the mass flux correlation was originally obtained by Batt et al
(1999) for sand particles. The two types of sand used in these tests had mass median particle size
of 180 microns, and 250 microns. Sand particles are compact in shape and have a particle density
of 2600 kg/m3. The free stream velocity used in these tests were nearly constant throughout each
test and ranged from 30 to 100 m/s.
This correlation also provided favorable prediction of the NIOSH data for coal dust / rock dust
mixtures with coarse as well as fine particle size (i.e. 80% smaller than 74 microns). NIOSH uses
particle density of 1330 kg/m3 for coal dust and 2750 kg/m3 for rock dust. The free stream
velocities recorded in NIOSH tests were highly transient pulses induced by the primary
explosion and ranged from 0 to above 200 m/s.
As also discussed in the previous chapter, a limited set of cornstarch entrainment data were
available from the NGFA tests, and provided a good agreement with the mass flux correlation. It
should be noted that cornstarch is made up of much finer particles that have a mass mean size of
15 microns and particle density of 1550 kg/m3. The free stream velocities recorded in NGFA
tests were transient pulses induced by the primary explosion and were estimated to range from 0
to 27 m/s.
Additional tests employing lower density (e.g. wood dust with approximately 500 kg/m3 particle
density), and higher density (e.g. iron dust with approximately 7800 kg/m3 particle density) will
be beneficial.
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The mass flux correlation employed in the strawman method accounts for the effect of
nonspherical shaped particles, through a correction factor for the threshold velocity. This effect
was introduced in an ad hoc fashion, and needs to be validated. The form of the mass flux
equation reveals that nonspherical shape effect becomes more pronounced in lower free stream
velocities. This behavior intuitively makes sense but needs to be validated with additional tests in
the next phase of this project. Furthermore, the proposed form of the mass flux equation implies
that entrainment for nonspherical shaped particles will initiate at lower free stream velocities and
proceed at a higher rate than that for spherical particles. This behavior also needs to be tested and
either validated or adjusted appropriately.
Finally, the extension of the mass flux correlation to elevated surfaces with small streamwise
dimension needs to be validated.
4.2 Recommended test arrangement
For the sake of simplicity and data reliability, a one-dimensional large-scale test set up is
recommended. Similar to the NIOSH tests, a primary deflagration or a blast wave can be set up
at the closed end of a gallery. NIOSH tests were performed in a full-scale mine with a rather
large cross-sectional area (20 ft by 7 ft). NGFA tests, on the other hand employed a test set up
that was 8 ft by 8 ft in cross-section. It is conceivable that testing in even a smaller scale can
produce good results. However, the minimum acceptable dimensions will depend how the air
pulse is generated and its duration. A driver system producing a weaker negative phase will be
desirable. It is also recommended that the construction of the walls and floor of the selected
facility should not be conducive to transmission of mechanical shocks that can be caused by the
initiating event. The length and the boundary conditions of the test facility are important factors
that must be considered when selecting or constructing a test facility.
Carefully formed dust beds can be placed on the floor and short span elevated surfaces at
sufficiently far downstream locations. The free stream velocity and static pressure transient need
to be recorded at each dust bed station. Free stream velocity should be measured near the center
of the cross-section, using calibrated probes that have response time fast enough to capture the
time variation of the free stream velocity faithfully. If a primary deflagration is used to create the
velocity transient, care must be exercised to ensure that flames do not ignite the dust beds.
In these tests, the peak free stream velocity should be varied from slightly above the threshold
value to at least 100 m/s. At least three replicate tests for each condition will be desirable.
As in NIOSH tests, total dust entrainment can be measured from the difference in the dust bed
thicknesses before and after the primary event. Preferably, the dust deposits are weighed before
and after each test, resulting in a determination of the mass removal. If the selected facility has
the capability to map the time resolved suspended dust concentration and velocity over the flow
field, dust entrainment mass flux can be deduced.
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It may be possible to get these tests performed at NIOSH for a little or no cost to the Fire
Protection Research Foundation under the NORA Intramural Research Program.
4.3 Recommended Test Matrix
The following test matrix is envisioned.
Ì
Ì
Ì
Ì
Ì
Peak free stream velocity: 15 m/s, 30 m/s, 60 m/s, and 100 m/s or higher.
Velocity pulse duration: preferably long, and to be decided based on available test
setup details.
Combustible dusts: wood dust, iron dust, tissue dust (or flocking fibers), aluminum
flakes.
Dust layer thickness: two to three thicknesses to be selected based on velocity pulse
duration and particle density.
Elevated surface span: representative dimensions of I-beam and roof support
structures. 4”, 12” and 24” are recommended.
By prudent placement of the beds, floor dust entrainment and elevated surface entrainment data
can be generated simultaneously in each test. The test matrix may be modified as data becomes
available.
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V
Acknowledgements
This work was made possible by the Fire Protection Research Foundation (an affiliate of the
National Fire Protection Association). The author is indebted to the companies who provided the
funding for this project through the Research Foundation, and to the project technical panel
members for many valuable suggestions. Special thanks go to Kathleen Almand, Henry Febo,
Walt Frank, and Sam Rodgers for serving on the special task group. The author is also grateful to
Marcia Harris of NIOSH and Michael Sapko of Sapko Consulting Inc. for many valuable
discussions, and for making unpublished NIOSH data available to him.
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VI
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Behind Shock Wave for Different Dust Layer Thicknesses,” 5th ISFEH
Zydak, Przemyslaw, Rudolf Klemens (2007), “Modelling Of Dust Lifting Process Behind
Propagating Shock Wave,” Journal of Loss Prevention in the Process Industries, 20, pp. 417–
426.
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APPENDIX A
Ad Hoc Methods to Characterize Material Dustiness and Entrainability
A menu of simple tests which have been devised to classify or screen powder properties are
introduced. These tests, intuitively believed to relate to the problem at hand, can be grouped into
the following four categories: (1) particle characterization; (2) cohesion tests; (3) terminal
velocity tests, and (4) dispersibility tests.
A.1 Particle Characterization
Particle Size and Shape:
In most powders, there is a wide gamut of particle sizes and shapes. For irregular particles (as
would be the case for most ground powders), the shape and size are difficult to characterize.
Therefore, the approach has been to define a size based on a parameter of great importance for a
given application. For example, for paint pigments, the projected area; for chemical reaction the
total surface area is considered important; thus, particles are characterized by the projected area
diameter and the surface diameter, respectively. For the dust dispersion problem, an aerodynamic
drag diameter should be appropriate to characterize the cloud behavior. For the dust pick-up,
however, the choice of characteristic size is not as clear.
Particle Density:
The density of individual particles is determined by using pyknometers based on gas or liquid
displacement by known weight of the solid particles. If the particles are porous, the liquid will
not normally enter the pores because of the surface tension. Therefore, density values measured
by liquid and gas pyknometers differ and are called envelope density and true density,
respectively. For the dust entrainment problem, envelope density is probably more appropriate,
making liquid pyknometer methods preferable.
Bulk Density:
The bulk density of a material is the mass per unit volume of many particles of the material. For
most powders, bulk density depends on the degree of packing, so that it is customary to define an
“aerated (loose) bulk density,” and a “packed bulk density.” The aerated bulk density is generally
determined by gently filling a container, whereas the packed bulk density applies to powder that
has been packed by means of vibrating the container typically for 5 minutes. In bulk solids
handling, bulk density is believed to have no effect on material flowability. In entrainment
phenomenon, however, bulk density may play an important role.
Carr Compressibility:
Compressibility is defined as the ratio of the difference between packed and aerated densities
normalized by the packed density (ASTM D6393). Generally, the more compressible the
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material, the less flowable it will be. According to Carr (1965), the borderline for free flowing to
non-free flowing is about 20% compressibility. In terms of the microscopic properties,
compressibility depends on particle shape, size distribution, deformability, surface area,
cohesion, and moisture content.
Carr Uniformity Coefficient:
This is a measure of the particle size distribution. Carr (1965a) and ASTM D6393 define it as the
ratio of the width of the sieve opening that will pass 60% of the sample by the width of the sieve
opening that will pass 10% of the sample. The conventional wisdom in bulk solid handling is
that the more uniform a mass of particles is in both size and shape, the more flowable it is likely
to be.
Moisture Content:
This is recognized as one of the important parameters affecting the entrainment of dust, since
both electrostatics and cohesive forces are strongly dependent on the moisture content. ASTM
has written extensive test procedures to determine the moisture content of a number of
substances, most of which are based on the weight loss after drying the sample at a specified
temperature for a specified period.
A.2 Cohesion Tests
Tackiness Test:
A rough test for tackiness is to try to form a ball of the material by rolling it between the palms
of the hands. If the ball falls apart, the material is not tacky (Kraus, 1980). Another qualitative
test for tackiness is to check whether the material, smeared onto a metal surface, will build up so
that it cannot slide off.
Carr Cohesion Test (ASTM D6393):
A somewhat more quantitative test has been used by Carr (1965 a). This procedure for apparent
surface cohesion involves determining the retention of material on a nest of 60 (220 um), 100
(147 um) and 200 (74 um) mesh screens, plus a bottom pan. A 2 gram sample presifted to minus
200 mesh is placed on the top screen (60—mesh) and the system is vibrated for 20 to 120
seconds depending on the bulk density of the material. At the end of the vibration period,
material left on each screen is weighed, and based on the weight distribution with respect to the
screen, a cohesion index is calculated.
Carr Angle of Repose (ASTM D6393):
This is the angle between the horizontal and the natural slope formed by a pile of material
dropped from some elevation. This angle, to a degree, should depend on the details of how the
material is being dropped. Although angle of repose is frequently used to characterize materials,
no standard test procedures exist. The angle of repose is a measure of friction between particles
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and is related to the potential flowability of material. At the microscopic level it is expected to
depend on particle shape, size, porosity, cohesion, fluidity and surface area.
Carr Angle of Fall (Angle of Slide):
After carefully building up the heap for the angle of repose measurement on a metallic plate, a
standard weight is dropped onto the plate from a prescribed height a predetermined number of
times. A new angle of repose results from the jarring. This angle is called the “angle of fall.” The
flattening of the heap may result from flow of the particles down the slope or the collapse of the
pile. The latter may indicate entrapped air within the heap. The angle of fall depends on the
fluidity, shape, size and uniformity of particles, entrapped air in the heap and cohesion.
Carr Angle of Difference (ASTM D6393):
This is the difference between angle of repose and the angle of fall, and it is believed to relate to
the potential for flooding or fluidity of a material. The angle of difference depends on the
fluidity, surface area and cohesion.
Carr Angle of Spatula (ASTM D6393):
This angle is measured by sticking a spatula with a sufficiently wide blade into the bottom of a
mass of the dry material and then lifting it straight up. A free—flowing material will form a
well—defined angle over the spatula, whereas a non—free-flowing material will form a number
of irregular angles over the blade. Carr (1965a) recommends the following procedure for
determining the angle of spatula: “First, angles to the horizontal are measured and an average
value taken. Then the spatula is tapped gently, producing a lower angle or angles of spatula that
are measured and again averaged. The average of the two averages is termed the angle of
spatula.”
Angle of spatula is determined by cohesion, particle surface area, size, shape, uniformity,
fluidity, porosity and deformability.
Shear Cell Test (ASTM D6128):
The shear cell (Jenike, 1964) consists of two rings, one sitting on top of the other, one secured on
a table. The volume inside the two rings is filled with powder to be tested, which is compressed
axially by loading the cover plate. The test determines the horizontal force required to move the
upper ring as a function of the compressive load. Based upon the cross- sectional area, a shear
stress is calculated, believed to represent the magnitude of the cohesive and frictional forces
between dust particles.
A.3 Terminal Velocity Tests
The terminal velocity of a particle or terminal velocity distribution of a powder is a well-defined
and measurable parameter. The reason for the inclusion of these tests in the intuitive approach
category is the intuitive relationship between the dust dispersibility and the terminal velocity.
The measurement techniques of terminal velocity of solid particles suspended in liquids are well
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developed and are frequently used to determine particle size distributions. A good review of this
subject is given by Allen (1975). However, there are only a few methods for terminal velocity
measurements in air, mainly due to the difficulty of dispersing powders.
Sedimentation Technique:
In this method, the powder is initially dispersed as a thin cloud near the top of a vertical tube
containing otherwise quiescent air. The dust cloud is allowed to settle in the tube, and the amount
of dust collected at the bottom is measured as a function of time. The height of the tube and the
time measured to collect various mass fractions are used to calculate the terminal velocity
distribution. The classical example of this method is the micromerograph originally developed
by Eadie and Payne (1956) to measure particle size distribution in the sub-sieve range. The
settling velocity apparatus developed by Ural (1989) is a modified and larger scale version of the
micromerograph.
Elutriation Technique:
This technique, mostly used for non-cohesive granular material, is based on introducing particles
into a vertical tube containing an upward air flow adjusted to the point where the particles are
held in a nearly stationary position (NMAB, 1982).
Centrifugal Technique:
The classical example of this technique is the Bahco microparticle classifier, described, for
example, by Allen (1975). This apparatus has been widely used since its adoption by the ASME
Power Test Codes (PTC28) as a standard method of measuring terminal velocity for the design
and evaluation of dust collection equipment. The sample is introduced into a spiral shaped air
current created by a hollow disk rotating at 3500 rpm. Air and dust are drawn through the cavity
in a radially inward direction against centrifugal forces. Separation into different size fractions is
made by altering the air velocity. The apparatus is calibrated using a standard dust with a known
terminal velocity distribution, provided by ASME.
A.4 Dispersibility Tests
Dispersibility can vaguely be defined as the ease of a powder to mix with air. If the ratio of the
mean particle spacing to particle size is much larger than one, the mixture is referred to as a dust
cloud, whereas if the ratio is of the order of one, the term aerated (or fluidized) powder is used.
Simple qualitative tests are performed to determine aeration and de—aeration characteristics of
powders. A few examples given in Kraus (1980) are as follows:
— Shake the material in a partially filled container and note if it swells in volume due to
aeration,
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— Stand the container of aerated material on a flat surface and note the time it takes to de-aerate
of its own accord,
— Rapidly tap a container of aerated material at a constant rate and note the time it takes to deaerate,
— Shake the material in a partially filled cardboard tube having a taped hole in the side near the
bottom. Stand the tube vertically on the edge of a table, remove the tape and note the trajectory
of the stream of material. A fluidized material will issue like water; a dead material may just
ooze and plug the orifice.
A simple and somewhat quantitative procedure for characterization of dispersibility is described
by Carr (1965a) and ASTM D6393. The apparatus used consists of a 4—in. I.D. plastic cylinder
13 in. long, supported vertically from a ring—stand 14 in. above a 14 in. diameter watch-glass. A
10 gram sample of material is dropped “en-masse” through the cylinder from a height of 24 in.
above the watch glass. Material remaining on the watch glass is weighed, and the difference
from the initial mass yields the amount dispersed during the fall.
A classical experiment of dispersibility was performed by Andreasen (1939). Two cubic
centimeters of powder were poured through a narrow slit into a vertical tube of 250 cm height
and 14.5 cm diameter. The particles were separated to some extent as they fell through the air,
and the percentage of powder, which had not settled to the bottom of the tube in 6 seconds, was
determined. Since the individual particles could not have reached the bottom in this time, the
author assumed that this figure represented the percentage of dispersed powder, which he called
dispersibility. Andreasen’s experiments have been criticized on the grounds that the unsettled
fraction also contained small aggregates. Some of his data is given here as Table A-1.
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TABLE A-1
DISPERSIBILITY OF SOME POWDERS MEASURED BY ANDREASEN (1939)
Lycopodium
Wood charcoal dust
Wood charcoal dust.
Aluminum powder
Talc
Carbon black
Potato starch
Graphite dust
Pulverized slate
Cement
Prepared chalk
Polydisperse silica dust (coarse)
Polydisperse silica dust (fine)
Isodisperse silica dust
Porcelain dust with fine fractions
Porcelain dust without fine
fractions removed
Particle
Radius
Limits um
12
0-25
0-7
0-15
0-20
0-.15(?)
0-35
0-25
0—25
0-45
0-6
11.5
8
5.6
7
2.7
1.1
0.145
Dispersi
bility (%)
100
85
23
66
57
147
27
17
13
5.5
1.5
21
8
68
83
145
50
52
21
12
-
5
ASTM developed two standards for characterization of the dustiness of powders. ASTM D54741(1980) Test Method for Index of Dustiness of Coal and Coke (Withdrawn 1986) was used to
evaluate the dustiness for coal and coke samples. ASTM D4331-84, Practice for Measuring
Effectiveness of Dedusting Agents for Powdered Chemicals (Withdrawn 1988), was used to
assess the effectiveness of dedusting agents for powdered chemicals.
The apparatus for ASTM D547 consisted of a metal cabinet 5 ft in height and 18 in. square,
inside dimensions, arranged with a cover and three horizontal slides and a drawer at the bottom.
The top slide was inserted 12 in. below the top of the cabinet and formed the compartment into
which the sample (50 lb) was placed. The other two slides were inserted together 24 in. above
the bottom (24 in. below the top slide) and were used to collect the settled dust after 2 and 10
minute intervals. Immediately before the test,
the upper slide was in the inserted position, whereas the lower slides were in withdrawn position.
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The test started with the quick withdrawal of the upper slide, allowing dust to drop into the
bottom drawer. Exactly 5 seconds later both lower slides were inserted. After the slides have
stood undisturbed for 2 minutes from the time of insertion, the upper one of the two lower slides
was withdrawn. The second lower slide was withdrawn after an additional 8 minutes has elapsed.
Two dustiness indices (coarse dust and float dust) were defined, based on the weight of the
samples on these two slides. ASTM requires a better than 20% reproducibility for the
measurements.
ASTM Test D4331 used a 3 in. plastic tubing (2 7/8 in. I.D.) 18 in. long as a fluidizing
environment. The tube was held vertically while a constant air flow rate corresponding to 6 cm/s
bulk velocity in the tube was supplied from the bottom. The top was covered with a partially
open (27%) cap. Also located at the top is a 5/16 in. I.D. sampling probe with a constant suction
velocity pump through a dust filter. During the test, the tube was vibrated at 29,000 rpm. The
standard called for a 200 g sample and 20 minute exposure. The amount of dust collected in the
filter during this time was used as a relative measure of dustiness.
Another widely used method of dispersibility characterization is to dump a known quantity of
material into a volume equipped with a high volume air sampler at the top. The ratio of the mass
of the powder collected by the sampler to the mass of the material handled is used as a measure
of the dustiness of the material. This method is used for comparison purposes, since the results
are dependent on the test apparatus and procedures. An example of this method can be found in
Lundgren and Rangaraj (1986).
Recently VDI 2263 (part 9) published a standard test method to determine dustiness of bulk
materials. A metering device conveys the sample into a measuring chamber at constant volume
flow rate. The concentration of the dust cloud forming in the measuring chamber is recorded as a
function of time. The standard calls the average of the measured dust concentration (averaged
over the test duration) the dustiness coefficient, S. Material is classified into one of the six
dustiness groups based on the value of the dustiness coefficient as shown below.
VDI Dustiness Group
1
2
3
4
5
6
Dustiness Index (g/m3)
LT 1
1 to 5
5 to 10
10 to 20
20 to 50
GT 50
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APPENDIX B
Alternative Mechanism on Dust Cloud Generation
A Panel member requested consideration of vibration or “Elastic Rebound” mechanism, shown
below as promoted in some NFPA training publications. Even though this topic is beyond the
scope of this project, an additional literature survey is conducted upon the Panel request.
Search was performed by querying Science Direct for the following keywords:
dust cloud generation mechanical vibration
“dust layer” "mechanical shock"
"dust cloud" "mechanical shock"
"dust cloud" "mechanical vibration"
"dust layer" "mechanical vibration"
"powder" "mechanical vibration"
"powder layer" "vibratory"
"dust layer" "vibratory"
"powder layer" "mechanical impact"
"powder layer" "mechanical shock"
"dust cloud" "mechanical impact"
"powder cloud" "mechanical impact"
"powder cloud" "mechanical shock"
Only Relevant mention found in a 1984 Eckhoff article:
HOW CAN DUST CLOUDS BE GENERATED AND IGNITED IN LARGE SILO CELLS? This question
certainly has more than one answer. In case the main material to be stored in the silo is in itself
sufficiently fine to give explosible clouds in air, explosible dust clouds are most likely to arise, at least
transiently, somewhere in the silo whenever new material is discharged into it, whether pneumatically or
mechanically. If the main material is coarse, such as grain, explosible dust clouds may be generated by
unburnt dust being blown into the silo by preceding explosions elsewhere in the plant. Dust could, for
example, be injected through the various openings close to the silo top. Injection through the hopper exit
at the bottom seems a more unlikely scenario. Another process of dust cloud generation could be that
dust layers, which have accumulated on the inside of the silo wall and roof, are disturbed and dispersed
into a cloud by air blasts or mechanical vibrations induced, for example, by preceding explosions
elsewhere in the plant.
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Other interesting but hardly useful papers included:
•
•
•
•
•
•
•
•
•
•
P. C. Arnold And K. S. Kaaden (1977), “Reducing Hopper Wall Friction By Mechanical Vibration,”
Powder Technology, 16, pp. 63 – 66
Diego Barletta, Giorgio Donsi, Giovanna Ferrari, Massimo Poletto, Paola Russo (2008), “The Effect Of
Mechanical Vibration On Gas Fluidization Of A Fine Aeratable Powder,” Chemical Engineering
Research And Design, 86 pp. 359–369.
Edward K. Levy, Brian Celeste (2006), “Combined Effects Of Mechanical And Acoustic Vibrations On
Fluidization Of Cohesive Powders,” Powder Technology, 163, pp. 41–50.
Norikazu Maeno And Kouichi Nishimura (1979), “Fluidization Of Snow,” Cold Regions Science And
Technology, 1, pp. 109-120.
Jozef S. Pastuszka (2009) “Emission Of Airborne Fibers From Mechanically Impacted Asbestos-Cement
Sheets And Concentration Of Fibrous Aerosol In The Home Environment In Upper Silesia, Poland,”
Journal Of Hazardous Materials 162, 1171–1177.
A.W. Roberts And O. J. Scott, “An Investigation Into The Effects Of Sinusoidal And Random Vibrations
On The Strength And Flow Properties Of Bulk Solids,” Powder Technology, 21. pp. 45 - 53.
P. H. Gregory And Maureen E. Lacey (1963), “Liberation Of Spores From Mouldy Hay,” Trans. Brit.
Mycol. Soc. 46 (1),73-80.
Gyorgy Ratkai (1976) “Particle Flow And Mixing In Vertically Vibrated Beds,” Powder Technology. 15,
pp. 187 - 192
Th. Kollmann And J. Tomas (2001) “Vibrational Flow Of Cohesive Powders,” Handbook Of Conveying
And Handling Of Particulate Solids, pp. 45-56.
Chunbao Xu, And Jesse Zhu (2005), “Experimental And Theoretical Study On The Agglomeration
Arising From Fluidization Of Cohesive Particles—Effects Of Mechanical Vibration,” Chemical
Engineering Science 60 pp. 6529 – 6541
Interestingly, the last paper listed above concludes:
The experimental results prove that mechanical vibration can significantly reduce both the average size
and the degree of the size-segregation of the agglomerates throughout the whole bed. However, the
experiments also reveal that the mean agglomerate size decreases initially with the vibration intensity,
but increases gradually as the vibration intensity exceeds a critical value. This suggests that the
vibration cannot only facilitate breaking the agglomerates due to the increased agglomerate collision
energy but can also favour the growth of the agglomerates due to the enhanced contacting probability
between particles and/or agglomerates.
The so-called “Elastic Rebound” mechanism was also analyzed by mating a bursting sphere
model with a single degree of freedom structural dynamic response model. For the typical “Spec
building” structural parameters, it was demonstrated that the subject mechanism does not appear
to be credible. This analysis will be published elsewhere.
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